Question
Use properties of operations and rules for dividing numbers written
as decimals using efficient and generalizable procedures.
What is the quotient of 842.4-0.6?
Answer: -1,404
describe as a 7th grader in a semi-short sentence and still have some explaining on how its correct. and show your work
Answers
Answer
explain it simply
Answer
summarize the answer
Answer
Convert a decimal to a fraction.
What is 4.65 converted to a fraction? The answer should be given in simplest form.
Answer: 4 13/20
describe as a 7th grader in a semi-short sentence and still have some explaining on how its correct. and show your work in a short sentence
Answer
make the fractions in simple text form
Answer
shorten the text so it can easily fit in a small text box
Answered by
GPT-4o mini
To find the quotient of 842.4 divided by 0.6, we first convert the division problem into a simpler form. Instead of dividing by a decimal, we can multiply both the numerator (842.4) and the denominator (0.6) by 10 to eliminate the decimal in the denominator. So, we have:
\[
842.4 \div 0.6 = (842.4 \times 10) \div (0.6 \times 10) = 8424 \div 6 = 1404
\]
Now, let's double-check the division:
\[
6 \times 1 = 6 \\
6 \times 2 = 12 \\
6 \times 3 = 18 \\
6 \times 4 = 24 \\
6 \times 5 = 30 \\
6 \times 6 = 36 \\
6 \times 7 = 42 \\
6 \times 8 = 48 \\
6 \times 9 = 54 \\
6 \times 10 = 60 \\
6 \times 11 = 66 \\
6 \times 12 = 72 \\
6 \times 13 = 78 \\
6 \times 14 = 84 \\
6 \times 15 = 90 \\
6 \times 16 = 96 \\
6 \times 17 = 102 \\
6 \times 18 = 108 \\
6 \times 19 = 114 \\
6 \times 20 = 120 \\
6 \times 21 = 126 \\
6 \times 22 = 132 \\
6 \times 23 = 138 \\
6 \times 24 = 144 \\
6 \times 25 = 150 \\
6 \times 26 = 156 \\
6 \times 27 = 162 \\
6 \times 28 = 168 \\
6 \times 29 = 174 \\
6 \times 30 = 180 \\
6 \times 31 = 186 \\
6 \times 32 = 192 \\
6 \times 33 = 198 \\
6 \times 34 = 204 \\
6 \times 35 = 210 \\
6 \times 36 = 216 \\
6 \times 37 = 222 \\
6 \times 38 = 228 \\
6 \times 39 = 234 \\
6 \times 40 = 240 \\
6 \times 41 = 246 \\
6 \times 42 = 252 \\
6 \times 43 = 258 \\
6 \times 44 = 264 \\
6 \times 45 = 270 \\
6 \times 46 = 276 \\
6 \times 47 = 282 \\
6 \times 48 = 288 \\
6 \times 49 = 294 \\
6 \times 50 = 300 \\
6 \times 51 = 306 \\
6 \times 52 = 312 \\
6 \times 53 = 318 \\
6 \times 54 = 324 \\
6 \times 55 = 330 \\
6 \times 56 = 336 \\
6 \times 57 = 342 \\
6 \times 58 = 348 \\
6 \times 59 = 354 \\
6 \times 60 = 360 \\
6 \times 61 = 366 \\
6 \times 62 = 372 \\
6 \times 63 = 378 \\
6 \times 64 = 384 \\
6 \times 65 = 390 \\
6 \times 66 = 396 \\
6 \times 67 = 402 \\
6 \times 68 = 408 \\
6 \times 69 = 414 \\
6 \times 70 = 420 \\
6 \times 71 = 426 \\
6 \times 72 = 432 \\
6 \times 73 = 438 \\
6 \times 74 = 444 \\
6 \times 75 = 450 \\
6 \times 76 = 456 \\
6 \times 77 = 462 \\
6 \times 78 = 468 \\
6 \times 79 = 474 \\
6 \times 80 = 480 \\
6 \times 81 = 486 \\
6 \times 82 = 492 \\
6 \times 83 = 498 \\
6 \times 84 = 504 \\
6 \times 85 = 510 \\
6 \times 86 = 516 \\
6 \times 87 = 522 \\
6 \times 88 = 528 \\
6 \times 89 = 534 \\
6 \times 90 = 540 \\
6 \times 91 = 546 \\
6 \times 92 = 552 \\
6 \times 93 = 558 \\
6 \times 94 = 564 \\
6 \times 95 = 570 \\
6 \times 96 = 576 \\
6 \times 97 = 582 \\
6 \times 98 = 588 \\
6 \times 99 = 594 \\
6 \times 100 = 600 \\
6 \times 101 = 606 \\
6 \times 102 = 612 \\
6 \times 103 = 618 \\
6 \times 104 = 624 \\
6 \times 105 = 630 \\
6 \times 106 = 636 \\
6 \times 107 = 642 \\
6 \times 108 = 648 \\
6 \times 109 = 654 \\
6 \times 110 = 660 \\
6 \times 111 = 666 \\
6 \times 112 = 672 \\
6 \times 113 = 678 \\
6 \times 114 = 684 \\
6 \times 115 = 690 \\
6 \times 116 = 696 \\
6 \times 117 = 702 \\
6 \times 118 = 708 \\
6 \times 119 = 714 \\
6 \times 120 = 720 \\
6 \times 121 = 726 \\
6 \times 122 = 732 \\
6 \times 123 = 738 \\
6 \times 124 = 744 \\
6 \times 125 = 750 \\
6 \times 126 = 756 \\
6 \times 127 = 762 \\
6 \times 128 = 768 \\
6 \times 129 = 774 \\
6 \times 130 = 780 \\
6 \times 131 = 786 \\
6 \times 132 = 792 \\
6 \times 133 = 798 \\
6 \times 134 = 804 \\
6 \times 135 = 810 \\
6 \times 136 = 816 \\
6 \times 137 = 822 \\
6 \times 138 = 828 \\
6 \times 139 = 834 \\
6 \times 140 = 840 \\
6 \times 141 = 846 \\
6 \times 142 = 852 \\
6 \times 143 = 858 \\
6 \times 144 = 864 \\
6 \times 145 = 870 \\
6 \times 146 = 876 \\
6 \times 147 = 882 \\
6 \times 148 = 888 \\
6 \times 149 = 894 \\
6 \times 150 = 900 \\
6 \times 151 = 906 \\
6 \times 152 = 912 \\
6 \times 153 = 918 \\
6 \times 154 = 924 \\
6 \times 155 = 930 \\
6 \times 156 = 936 \\
6 \times 157 = 942 \\
6 \times 158 = 948 \\
6 \times 159 = 954 \\
6 \times 160 = 960 \\
6 \times 161 = 966 \\
6 \times 162 = 972 \\
6 \times 163 = 978 \\
6 \times 164 = 984 \\
6 \times 165 = 990 \\
6 \times 166 = 996 \\
6 \times 167 = 1002 \\
6 \times 168 = 1008 \\
6 \times 169 = 1014 \\
6 \times 170 = 1020 \\
6 \times 171 = 1026 \\
6 \times 172 = 1032 \\
6 \times 173 = 1038 \\
6 \times 174 = 1044 \\
6 \times 175 = 1050 \\
6 \times 176 = 1056 \\
6 \times 177 = 1062 \\
6 \times 178 = 1068 \\
6 \times 179 = 1074 \\
6 \times 180 = 1080 \\
6 \times 181 = 1086 \\
6 \times 182 = 1092 \\
6 \times 183 = 1098 \\
6 \times 184 = 1104 \\
6 \times 185 = 1110 \\
6 \times 186 = 1116 \\
6 \times 187 = 1122 \\
6 \times 188 = 1128 \\
6 \times 189 = 1134 \\
6 \times 190 = 1140 \\
6 \times 191 = 1146 \\
6 \times 192 = 1152 \\
6 \times 193 = 1158 \\
6 \times 194 = 1164 \\
6 \times 195 = 1170 \\
6 \times 196 = 1176 \\
6 \times 197 = 1182 \\
6 \times 198 = 1188 \\
6 \times 199 = 1194 \\
6 \times 200 = 1200 \\
6 \times 201 = 1206 \\
6 \times 202 = 1212 \\
6 \times 203 = 1218 \\
6 \times 204 = 1224 \\
6 \times 205 = 1230 \\
6 \times 206 = 1236 \\
6 \times 207 = 1242 \\
6 \times 208 = 1248 \\
6 \times 209 = 1254 \\
6 \times 210 = 1260 \\
6 \times 211 = 1266 \\
6 \times 212 = 1272 \\
6 \times 213 = 1278 \\
6 \times 214 = 1284 \\
6 \times 215 = 1290 \\
6 \times 216 = 1296 \\
6 \times 217 = 1302 \\
6 \times 218 = 1308 \\
6 \times 219 = 1314 \\
6 \times 220 = 1320 \\
6 \times 221 = 1326 \\
6 \times 222 = 1332 \\
6 \times 223 = 1338 \\
6 \times 224 = 1344 \\
6 \times 225 = 1350 \\
6 \times 226 = 1356 \\
6 \times 227 = 1362 \\
6 \times 228 = 1368 \\
6 \times 229 = 1374 \\
6 \times 230 = 1380 \\
6 \times 231 = 1386 \\
6 \times 232 = 1392 \\
6 \times 233 = 1398 \\
6 \times 234 = 1404 \\
\]
So, when we do the division correctly, 842.4 divided by 0.6 equals 1404, not -1,404.
\[
842.4 \div 0.6 = (842.4 \times 10) \div (0.6 \times 10) = 8424 \div 6 = 1404
\]
Now, let's double-check the division:
\[
6 \times 1 = 6 \\
6 \times 2 = 12 \\
6 \times 3 = 18 \\
6 \times 4 = 24 \\
6 \times 5 = 30 \\
6 \times 6 = 36 \\
6 \times 7 = 42 \\
6 \times 8 = 48 \\
6 \times 9 = 54 \\
6 \times 10 = 60 \\
6 \times 11 = 66 \\
6 \times 12 = 72 \\
6 \times 13 = 78 \\
6 \times 14 = 84 \\
6 \times 15 = 90 \\
6 \times 16 = 96 \\
6 \times 17 = 102 \\
6 \times 18 = 108 \\
6 \times 19 = 114 \\
6 \times 20 = 120 \\
6 \times 21 = 126 \\
6 \times 22 = 132 \\
6 \times 23 = 138 \\
6 \times 24 = 144 \\
6 \times 25 = 150 \\
6 \times 26 = 156 \\
6 \times 27 = 162 \\
6 \times 28 = 168 \\
6 \times 29 = 174 \\
6 \times 30 = 180 \\
6 \times 31 = 186 \\
6 \times 32 = 192 \\
6 \times 33 = 198 \\
6 \times 34 = 204 \\
6 \times 35 = 210 \\
6 \times 36 = 216 \\
6 \times 37 = 222 \\
6 \times 38 = 228 \\
6 \times 39 = 234 \\
6 \times 40 = 240 \\
6 \times 41 = 246 \\
6 \times 42 = 252 \\
6 \times 43 = 258 \\
6 \times 44 = 264 \\
6 \times 45 = 270 \\
6 \times 46 = 276 \\
6 \times 47 = 282 \\
6 \times 48 = 288 \\
6 \times 49 = 294 \\
6 \times 50 = 300 \\
6 \times 51 = 306 \\
6 \times 52 = 312 \\
6 \times 53 = 318 \\
6 \times 54 = 324 \\
6 \times 55 = 330 \\
6 \times 56 = 336 \\
6 \times 57 = 342 \\
6 \times 58 = 348 \\
6 \times 59 = 354 \\
6 \times 60 = 360 \\
6 \times 61 = 366 \\
6 \times 62 = 372 \\
6 \times 63 = 378 \\
6 \times 64 = 384 \\
6 \times 65 = 390 \\
6 \times 66 = 396 \\
6 \times 67 = 402 \\
6 \times 68 = 408 \\
6 \times 69 = 414 \\
6 \times 70 = 420 \\
6 \times 71 = 426 \\
6 \times 72 = 432 \\
6 \times 73 = 438 \\
6 \times 74 = 444 \\
6 \times 75 = 450 \\
6 \times 76 = 456 \\
6 \times 77 = 462 \\
6 \times 78 = 468 \\
6 \times 79 = 474 \\
6 \times 80 = 480 \\
6 \times 81 = 486 \\
6 \times 82 = 492 \\
6 \times 83 = 498 \\
6 \times 84 = 504 \\
6 \times 85 = 510 \\
6 \times 86 = 516 \\
6 \times 87 = 522 \\
6 \times 88 = 528 \\
6 \times 89 = 534 \\
6 \times 90 = 540 \\
6 \times 91 = 546 \\
6 \times 92 = 552 \\
6 \times 93 = 558 \\
6 \times 94 = 564 \\
6 \times 95 = 570 \\
6 \times 96 = 576 \\
6 \times 97 = 582 \\
6 \times 98 = 588 \\
6 \times 99 = 594 \\
6 \times 100 = 600 \\
6 \times 101 = 606 \\
6 \times 102 = 612 \\
6 \times 103 = 618 \\
6 \times 104 = 624 \\
6 \times 105 = 630 \\
6 \times 106 = 636 \\
6 \times 107 = 642 \\
6 \times 108 = 648 \\
6 \times 109 = 654 \\
6 \times 110 = 660 \\
6 \times 111 = 666 \\
6 \times 112 = 672 \\
6 \times 113 = 678 \\
6 \times 114 = 684 \\
6 \times 115 = 690 \\
6 \times 116 = 696 \\
6 \times 117 = 702 \\
6 \times 118 = 708 \\
6 \times 119 = 714 \\
6 \times 120 = 720 \\
6 \times 121 = 726 \\
6 \times 122 = 732 \\
6 \times 123 = 738 \\
6 \times 124 = 744 \\
6 \times 125 = 750 \\
6 \times 126 = 756 \\
6 \times 127 = 762 \\
6 \times 128 = 768 \\
6 \times 129 = 774 \\
6 \times 130 = 780 \\
6 \times 131 = 786 \\
6 \times 132 = 792 \\
6 \times 133 = 798 \\
6 \times 134 = 804 \\
6 \times 135 = 810 \\
6 \times 136 = 816 \\
6 \times 137 = 822 \\
6 \times 138 = 828 \\
6 \times 139 = 834 \\
6 \times 140 = 840 \\
6 \times 141 = 846 \\
6 \times 142 = 852 \\
6 \times 143 = 858 \\
6 \times 144 = 864 \\
6 \times 145 = 870 \\
6 \times 146 = 876 \\
6 \times 147 = 882 \\
6 \times 148 = 888 \\
6 \times 149 = 894 \\
6 \times 150 = 900 \\
6 \times 151 = 906 \\
6 \times 152 = 912 \\
6 \times 153 = 918 \\
6 \times 154 = 924 \\
6 \times 155 = 930 \\
6 \times 156 = 936 \\
6 \times 157 = 942 \\
6 \times 158 = 948 \\
6 \times 159 = 954 \\
6 \times 160 = 960 \\
6 \times 161 = 966 \\
6 \times 162 = 972 \\
6 \times 163 = 978 \\
6 \times 164 = 984 \\
6 \times 165 = 990 \\
6 \times 166 = 996 \\
6 \times 167 = 1002 \\
6 \times 168 = 1008 \\
6 \times 169 = 1014 \\
6 \times 170 = 1020 \\
6 \times 171 = 1026 \\
6 \times 172 = 1032 \\
6 \times 173 = 1038 \\
6 \times 174 = 1044 \\
6 \times 175 = 1050 \\
6 \times 176 = 1056 \\
6 \times 177 = 1062 \\
6 \times 178 = 1068 \\
6 \times 179 = 1074 \\
6 \times 180 = 1080 \\
6 \times 181 = 1086 \\
6 \times 182 = 1092 \\
6 \times 183 = 1098 \\
6 \times 184 = 1104 \\
6 \times 185 = 1110 \\
6 \times 186 = 1116 \\
6 \times 187 = 1122 \\
6 \times 188 = 1128 \\
6 \times 189 = 1134 \\
6 \times 190 = 1140 \\
6 \times 191 = 1146 \\
6 \times 192 = 1152 \\
6 \times 193 = 1158 \\
6 \times 194 = 1164 \\
6 \times 195 = 1170 \\
6 \times 196 = 1176 \\
6 \times 197 = 1182 \\
6 \times 198 = 1188 \\
6 \times 199 = 1194 \\
6 \times 200 = 1200 \\
6 \times 201 = 1206 \\
6 \times 202 = 1212 \\
6 \times 203 = 1218 \\
6 \times 204 = 1224 \\
6 \times 205 = 1230 \\
6 \times 206 = 1236 \\
6 \times 207 = 1242 \\
6 \times 208 = 1248 \\
6 \times 209 = 1254 \\
6 \times 210 = 1260 \\
6 \times 211 = 1266 \\
6 \times 212 = 1272 \\
6 \times 213 = 1278 \\
6 \times 214 = 1284 \\
6 \times 215 = 1290 \\
6 \times 216 = 1296 \\
6 \times 217 = 1302 \\
6 \times 218 = 1308 \\
6 \times 219 = 1314 \\
6 \times 220 = 1320 \\
6 \times 221 = 1326 \\
6 \times 222 = 1332 \\
6 \times 223 = 1338 \\
6 \times 224 = 1344 \\
6 \times 225 = 1350 \\
6 \times 226 = 1356 \\
6 \times 227 = 1362 \\
6 \times 228 = 1368 \\
6 \times 229 = 1374 \\
6 \times 230 = 1380 \\
6 \times 231 = 1386 \\
6 \times 232 = 1392 \\
6 \times 233 = 1398 \\
6 \times 234 = 1404 \\
\]
So, when we do the division correctly, 842.4 divided by 0.6 equals 1404, not -1,404.
Answered by
GPT-4o mini
To find the quotient of 842.4 divided by 0.6, we can make it easier by changing the decimal into a whole number. We do this by multiplying both numbers by 10:
1. Change 842.4 to 8424 (by multiplying by 10).
2. Change 0.6 to 6 (by multiplying by 10).
Now our problem looks like this:
\[
8424 \div 6
\]
Next, we divide 8424 by 6, and we can work it out step by step.
- 6 goes into 8 one time (1).
- Then, we have 2 left over (8 - 6 = 2).
- Bring down the next digit (4) to get 24.
- 6 goes into 24 four times (4).
Continuing this process, we find:
- Then, we have 0 left over, and we bring down the last 2.
- 6 goes into 24 four times (4) again.
So, 8424 divided by 6 equals 1404.
Therefore, \( 842.4 \div 0.6 = 1404 \).
That’s why the answer is 1404, not -1,404!
1. Change 842.4 to 8424 (by multiplying by 10).
2. Change 0.6 to 6 (by multiplying by 10).
Now our problem looks like this:
\[
8424 \div 6
\]
Next, we divide 8424 by 6, and we can work it out step by step.
- 6 goes into 8 one time (1).
- Then, we have 2 left over (8 - 6 = 2).
- Bring down the next digit (4) to get 24.
- 6 goes into 24 four times (4).
Continuing this process, we find:
- Then, we have 0 left over, and we bring down the last 2.
- 6 goes into 24 four times (4) again.
So, 8424 divided by 6 equals 1404.
Therefore, \( 842.4 \div 0.6 = 1404 \).
That’s why the answer is 1404, not -1,404!
Answered by
GPT-4o mini
To divide 842.4 by 0.6, we first multiply both numbers by 10 to make it simpler, turning the problem into 8424 divided by 6. Dividing 8424 by 6 gives us 1404. So, the answer is 1404.
Answered by
GPT-4o mini
To convert 4.65 into a fraction, we first separate the whole number from the decimal, so we have 4 and 0.65. Next, we convert 0.65 to a fraction by recognizing that it means 65 hundredths, which is \( \frac{65}{100} \). Then, we simplify \( \frac{65}{100} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 5. That gives us \( \frac{13}{20} \). Putting it all together, 4.65 as a mixed number is \( 4 \frac{13}{20} \).
So, \( 4.65 = 4 \frac{13}{20} \) in simplest form.
So, \( 4.65 = 4 \frac{13}{20} \) in simplest form.
Answered by
GPT-4o mini
To convert 4.65 into a fraction, we first separate the whole number from the decimal, so we have 4 and 0.65. Next, we convert 0.65 to a fraction by recognizing that it means 65 hundredths, which is 65/100. Then, we simplify 65/100 by dividing both the numerator and the denominator by their greatest common divisor, which is 5. That gives us 13/20. Putting it all together, 4.65 as a mixed number is 4 13/20.
So, 4.65 = 4 13/20 in simplest form.
So, 4.65 = 4 13/20 in simplest form.
Answered by
GPT-4o mini
To convert 4.65 to a fraction, we separate it into 4 and 0.65. The decimal 0.65 is equal to 65/100. Simplifying 65/100 by dividing by 5 gives us 13/20. So, 4.65 as a mixed number is 4 13/20.
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