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Subtract 9 7/10−6 1/4

. What is the difference?(1 point)
Responses

3 9/20

15 19/20

2 9/20

3 1/2

7 answers

To solve the subtraction \( 9 \frac{7}{10} - 6 \frac{1}{4} \), we can first convert the mixed numbers to improper fractions.

  1. Convert \( 9 \frac{7}{10} \) to an improper fraction: \[ 9 \frac{7}{10} = \frac{(9 \times 10) + 7}{10} = \frac{90 + 7}{10} = \frac{97}{10} \]

  2. Convert \( 6 \frac{1}{4} \) to an improper fraction: \[ 6 \frac{1}{4} = \frac{(6 \times 4) + 1}{4} = \frac{24 + 1}{4} = \frac{25}{4} \]

Now, we need a common denominator to subtract these fractions. The denominators are 10 and 4. The least common multiple of these numbers is 20.

  1. Convert both fractions to have a denominator of 20:

    • For \( \frac{97}{10} \): \[ \frac{97}{10} = \frac{97 \times 2}{10 \times 2} = \frac{194}{20} \]

    • For \( \frac{25}{4} \): \[ \frac{25}{4} = \frac{25 \times 5}{4 \times 5} = \frac{125}{20} \]

  2. Now, subtract the two fractions: \[ \frac{194}{20} - \frac{125}{20} = \frac{194 - 125}{20} = \frac{69}{20} \]

  3. Convert \( \frac{69}{20} \) back to a mixed number: \[ 69 \div 20 = 3 \text{ remainder } 9 \quad \text{so} \quad \frac{69}{20} = 3 \frac{9}{20} \]

Thus, the difference \( 9 \frac{7}{10} - 6 \frac{1}{4} \) is \( 3 \frac{9}{20} \).

The answer is: 3 9/20

Prairie Street is 3 7/8
miles long. Plains Avenue is 3 5/10
miles long. Ellis rides his bike the length of both Prairie Street and Plains Avenue. How many total miles does he ride?(1 point)
Responses

3/8

6 7/12

6 3/8

7 3/8

To find the total distance that Ellis rides his bike, we need to add the lengths of Prairie Street and Plains Avenue.

  1. Convert the mixed numbers to improper fractions.

    For Prairie Street \( 3 \frac{7}{8} \): \[ 3 \frac{7}{8} = \frac{(3 \times 8) + 7}{8} = \frac{24 + 7}{8} = \frac{31}{8} \]

    For Plains Avenue \( 3 \frac{5}{10} \): \[ 3 \frac{5}{10} = \frac{(3 \times 10) + 5}{10} = \frac{30 + 5}{10} = \frac{35}{10} = \frac{7}{2} \quad \text{(by simplifying)} \]

  2. To add these fractions, we need a common denominator. The least common multiple of 8 and 2 is 8.

    Convert \( \frac{7}{2} \) to have a denominator of 8: \[ \frac{7}{2} = \frac{7 \times 4}{2 \times 4} = \frac{28}{8} \]

  3. Now we can add the two fractions: \[ \frac{31}{8} + \frac{28}{8} = \frac{31 + 28}{8} = \frac{59}{8} \]

  4. Convert \( \frac{59}{8} \) back to a mixed number: \[ 59 \div 8 = 7 \quad \text{remainder } 3 \quad \text{so} \quad \frac{59}{8} = 7 \frac{3}{8} \]

Thus, the total distance that Ellis rides is \( 7 \frac{3}{8} \) miles.

The answer is: 7 3/8

Explain why you cannot add or subtract fractions with unlike denominators while you can add or subtract fractions with like denominators. Include one or more real-world examples in your explanation. 5th grader words please!

Sure! Let's break it down in a way that's easy to understand.

When you add or subtract fractions, the bottom number (called the denominator) tells us how many equal parts something is divided into. If the denominators are the same (like in the fraction \( \frac{1}{4} + \frac{2}{4} \)), it means both fractions are talking about the same size of pieces. So, you can just add the top numbers (the numerators).

For example, if you have \( \frac{1}{4} \) of a pizza and your friend has \( \frac{2}{4} \) of the same pizza, together you have: \[ 1 + 2 = 3 \quad \text{(so you have \( \frac{3}{4} \) of the pizza).} \]

Now, when the denominators are different (like \( \frac{1}{4} + \frac{1}{2} \)), the pieces are not the same size. One piece is a quarter of a pizza, and the other is a half. You can't just add them because you wouldn't be comparing the same kinds of pieces.

To add these fractions, you have to change them so they have the same denominator first. For \( \frac{1}{4} \) and \( \frac{1}{2} \), we can change \( \frac{1}{2} \) into \( \frac{2}{4} \) so both fractions have 4 as the denominator. Then you can add them: \[ \frac{1}{4} + \frac{2}{4} = \frac{3}{4}. \]

Real-World Examples:

  1. Buying Candy: Let’s say you buy \( \frac{1}{3} \) of a pound of candy, and your friend buys \( \frac{1}{2} \) of a pound of candy. You can't just add those amounts directly since they're different sizes. You would need to change \( \frac{1}{2} \) to a fraction that has a denominator of 6 (which would be \( \frac{3}{6} \)). Now, you can add \( \frac{2}{6} \) and \( \frac{3}{6} \) together.

  2. Measuring Ingredients: When you're cooking and you have \( \frac{2}{5} \) of a cup of sugar and you want to add \( \frac{1}{3} \) of a cup of sugar, you can’t just combine those amounts right away. You need to find a common denominator, which is usually 15 in this case, to figure out how much sugar you really have together.

In summary, you can only add or subtract fractions with the same denominator because they represent the same size slices. When they're different, you need to make them alike first, so you can accurately find the total.

make it shorter

Sure! Here’s a shorter explanation:

You can only add or subtract fractions with the same bottom number (denominator) because that tells you the size of the pieces. For example, with \( \frac{1}{4} + \frac{2}{4} \), both fractions have the same size pieces, so you can just add the top numbers to get \( \frac{3}{4} \).

But if the fractions have different denominators, like \( \frac{1}{4} + \frac{1}{2} \), the pieces are different sizes, so you can't simply add them. You need to change them to have the same denominator first. For example, you can change \( \frac{1}{2} \) to \( \frac{2}{4} \) so you can add \( \frac{1}{4} + \frac{2}{4} \) to get \( \frac{3}{4} \).

Real-World Examples:

  1. Buying Candy: If you buy \( \frac{1}{3} \) of a pound and your friend buys \( \frac{1}{2} \), you can't add those directly since the parts are different sizes.

  2. Measuring Ingredients: If you have \( \frac{2}{5} \) of a cup of sugar and \( \frac{1}{3} \) of a cup, you need to find a common denominator to combine them accurately.

In summary, fractions need the same denominator to add or subtract because they must represent the same size pieces!