Asked by Vanrouge
Simplify 7 2/3 + - 5 1/4
Answers
Answered by
GPT 3.5
We can simplify the addition of mixed numbers by converting them into improper fractions.
To convert 7 2/3 to an improper fraction, we multiply the whole number (7) by the denominator of the fraction (3), and then add the numerator (2). This gives us (7 * 3 + 2) / 3 = 23/3.
Similarly, to convert -5 1/4 to an improper fraction, we multiply the whole number (-5) by the denominator of the fraction (4), and then add the numerator (1). This gives us (-5 * 4 + 1) / 4 = (-20 + 1) / 4 = -19/4.
Now, we can add the two improper fractions:
23/3 + (-19/4)
To add these fractions, we need a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
To make the denominators 12, we multiply the numerator and denominator of the first fraction by 4, and the numerator and denominator of the second fraction by 3:
(23/3) * (4/4) = 92/12
(-19/4) * (3/3) = -57/12
Now that we have a common denominator, we can add the fractions:
92/12 + (-57/12)
To add these fractions, we simply add the numerators while keeping the denominator the same:
(92 - 57) / 12 = 35/12
Therefore, 7 2/3 + - 5 1/4 simplifies to 35/12.
To convert 7 2/3 to an improper fraction, we multiply the whole number (7) by the denominator of the fraction (3), and then add the numerator (2). This gives us (7 * 3 + 2) / 3 = 23/3.
Similarly, to convert -5 1/4 to an improper fraction, we multiply the whole number (-5) by the denominator of the fraction (4), and then add the numerator (1). This gives us (-5 * 4 + 1) / 4 = (-20 + 1) / 4 = -19/4.
Now, we can add the two improper fractions:
23/3 + (-19/4)
To add these fractions, we need a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
To make the denominators 12, we multiply the numerator and denominator of the first fraction by 4, and the numerator and denominator of the second fraction by 3:
(23/3) * (4/4) = 92/12
(-19/4) * (3/3) = -57/12
Now that we have a common denominator, we can add the fractions:
92/12 + (-57/12)
To add these fractions, we simply add the numerators while keeping the denominator the same:
(92 - 57) / 12 = 35/12
Therefore, 7 2/3 + - 5 1/4 simplifies to 35/12.
Answered by
GPT 3.5
To simplify 7 2/3 + -5 1/4 as a mixed number, we need to first find the sum as an improper fraction.
We already found that 7 2/3 can be expressed as the improper fraction 23/3, and -5 1/4 can be expressed as the improper fraction -19/4.
To add these improper fractions, we need a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
To convert 23/3 to have a denominator of 12, we multiply the numerator and denominator by 4:
(23/3) × (4/4) = 92/12
To convert -19/4 to have a denominator of 12, we multiply the numerator and denominator by 3:
(-19/4) × (3/3) = -57/12
Now, we can add the fractions:
92/12 + (-57/12) = 35/12
To express 35/12 as a mixed number, we divide the numerator (35) by the denominator (12). The quotient will be the whole number, and the remainder will be the numerator of the fraction.
35 ÷ 12 = 2 remainder 11
Therefore, the simplified form of 7 2/3 + -5 1/4 as a mixed number is 2 11/12.
We already found that 7 2/3 can be expressed as the improper fraction 23/3, and -5 1/4 can be expressed as the improper fraction -19/4.
To add these improper fractions, we need a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
To convert 23/3 to have a denominator of 12, we multiply the numerator and denominator by 4:
(23/3) × (4/4) = 92/12
To convert -19/4 to have a denominator of 12, we multiply the numerator and denominator by 3:
(-19/4) × (3/3) = -57/12
Now, we can add the fractions:
92/12 + (-57/12) = 35/12
To express 35/12 as a mixed number, we divide the numerator (35) by the denominator (12). The quotient will be the whole number, and the remainder will be the numerator of the fraction.
35 ÷ 12 = 2 remainder 11
Therefore, the simplified form of 7 2/3 + -5 1/4 as a mixed number is 2 11/12.
Answered by
GPT 3.5
To evaluate 32 + (-73.1), we simply add the two numbers together:
32 + (-73.1) = -41.1
Therefore, 32 + (-73.1) equals -41.1.
32 + (-73.1) = -41.1
Therefore, 32 + (-73.1) equals -41.1.
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