Question

Whats the answer to these? (These are called Proper fractions.)

Jeremiah ran for 3/10 of a mile and then walked another 2/5 of a mile. How far did he travel in all?

Daniel read 4/5 books and Edgar read 1/2 books. How many more books did Daniel read than Edgar?

Jared drove 2/8 miles to the restaurant. He drove another 1/4 miles to the mall. How many miles did he drive in all?​

Answer 1

Answer to the first question: 7/10ths of a mile

Explaination: When adding fractions, you need to have a common denominator. Since dividing 3/10 by 2 to get a denominator of 5 makes 3 a decimal, it's easier to multiply 2/5 by 2 to get a denominator of 10. You do the same to the top that you do to the bottom: $\frac{2*2}{5*2} = \frac{4}{10}$. From there, just add 4/10 and 3/10 to get the answer: 7/10ths of a mile.

Answer to the second question: Daniel read three (3/10) more books

Explaination: Since you can't evenly multiply 5 or 2 to get the opposite number, it's easier to multiply to the lowest common multiple. The easiest way to find that is to multiply both denominators (5*2=10). You'll have to multiply the numerator by the same amount you multipled the denominator by. For Daniel, that would mean: $\frac{4*2}{5*2} = \frac{8}{10}$. For Edgar, that would mean: $\frac{1*5}{2*5} = \frac{5}{10}$. So, Daniel read 3 more books than Edgar.

Answer to the third question: 2/4 mile (or 1/2 a mile)

Explaination: 2/8 can be simplified, by dividing the top and bottom by 2, resulting in 1/4. Since both fractions have the same denominator (/4), you can add them to get 2/4ths. This can be simplified further to half (1/2) a mile.

Answer 2

Answer and Step-by-step explanation:

1. Convert $\frac{2}{5}$ to have a denominator of 10.

$\frac{2}{5}$ × $\frac{2}{2}$ = $\frac{4}{10}$

$\frac{3}{10} + \frac{4}{10} = \frac{7}{10}$

Jeremiah ran $\frac{7}{10}$ of a mile in total.

2. Convert the denominators of all the fractions to have a 10.

$\frac{1}{2}$ × $\frac{5}{5} =\frac{5}{10}$

$\frac{4}{5}$ × $\frac{2}{2} = \frac{8}{10}$

Daniel read $\frac{3}{10}$ more books than Edgar, since 8 books is more than 5 books by 3 books.

3. Convert $\frac{1}{4}$ to have a denominator of 8.

$\frac{1}{4}$ × $\frac{2}{2} = \frac{2}{8}$

$\frac{2}{8} +\frac{2}{8}= \frac{4}{8}, or\frac{1}{2}$

Jared drove $\frac{4}{8}$, or $\frac{1}{2}$ miles in total.

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