Math / Numbers & Operations

Question5th Grade: Unit 4 Study Guide - Test on Thursday, DeC. 17, 24
3. Which expression is true? How do you know? A. $\frac{13}{8}<\frac{5}{3}<\frac{7}{4}$ B. $\frac{13}{8}>\frac{5}{3}>\frac{7}{4}$

Studdy Solution

STEP 1

What is this asking? Which of these lists of fractions is in the correct order, from smallest to largest or largest to smallest? Watch out! Don't just guess based on how the fractions look.
We need to actually compare them!

STEP 2

1. Convert to a Common Denominator
2. Compare the Fractions
3. Determine the Correct Order

STEP 3

Let's find the least common multiple (LCM) of the denominators: 8, 3, and 4.
The LCM is the smallest number that all three denominators divide into evenly.
We can list multiples of each number until we find a common one.
Multiples of 8 are 8, 16, 24, 32... Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27... Multiples of 4 are 4, 8, 12, 16, 20, 24, 28... So, our LCM is 24!

STEP 4

Now, we'll convert each fraction so it has a denominator of 24.
For $\frac{13}{8}$ , we multiply the top and bottom by 3 (because $8 \cdot 3 = 24$ ): $\frac{13}{8} \cdot \frac{3}{3} = \frac{39}{24}$ .
For $\frac{5}{3}$ , we multiply the top and bottom by 8 (because $3 \cdot 8 = 24$ ): $\frac{5}{3} \cdot \frac{8}{8} = \frac{40}{24}$ .
For $\frac{7}{4}$ , we multiply the top and bottom by 6 (because $4 \cdot 6 = 24$ ): $\frac{7}{4} \cdot \frac{6}{6} = \frac{42}{24}$ .

STEP 5

Now that all the fractions have the same denominator (24), we can compare them by looking at their numerators.
We have $\frac{39}{24}$ , $\frac{40}{24}$ , and $\frac{42}{24}$ .

STEP 6

The numerators are 39, 40, and 42.
Since $39 < 40 < 42$ , we know that $\frac{39}{24} < \frac{40}{24} < \frac{42}{24}$ .

STEP 7

Substituting back the original fractions, we get $\frac{13}{8} < \frac{5}{3} < \frac{7}{4}$ .

STEP 8

This matches option A!

STEP 9

The correct expression is A: $\frac{13}{8} < \frac{5}{3} < \frac{7}{4}$ .

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Question5th Grade: Unit 4 Study Guide - Test on Thursday, DeC. 17, 24
3. Which expression is true? How do you know? A. $\frac{13}{8}<\frac{5}{3}<\frac{7}{4}$ B. $\frac{13}{8}>\frac{5}{3}>\frac{7}{4}$

Studdy Solution

STEP 1

What is this asking? Which of these lists of fractions is in the correct order, from smallest to largest or largest to smallest? Watch out! Don't just guess based on how the fractions look.
We need to actually compare them!

STEP 2

1. Convert to a Common Denominator
2. Compare the Fractions
3. Determine the Correct Order

STEP 3

STEP 4

STEP 5

Now that all the fractions have the same denominator (24), we can compare them by looking at their numerators.
We have $\frac{39}{24}$ , $\frac{40}{24}$ , and $\frac{42}{24}$ .

STEP 6

The numerators are 39, 40, and 42.
Since $39 < 40 < 42$ , we know that $\frac{39}{24} < \frac{40}{24} < \frac{42}{24}$ .

STEP 7

Substituting back the original fractions, we get $\frac{13}{8} < \frac{5}{3} < \frac{7}{4}$ .

STEP 8

This matches option A!

STEP 9

The correct expression is A: $\frac{13}{8} < \frac{5}{3} < \frac{7}{4}$ .

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Question5th Grade: Unit 4 Study Guide - Test on Thursday, DeC. 17, 243. Which expression is true? How do you know? A. 138<53<74\frac{13}{8}<\frac{5}{3}<\frac{7}{4}813​<35​<47​ B. 138>53>74\frac{13}{8}>\frac{5}{3}>\frac{7}{4}813​>35​>47​

Studdy Solution

STEP 1

What is this asking? Which of these lists of fractions is in the correct order, from smallest to largest or largest to smallest? Watch out! Don't just guess based on how the fractions *look*.We need to actually compare them!

STEP 2

1. Convert to a Common Denominator2. Compare the Fractions3. Determine the Correct Order

STEP 3

STEP 4

STEP 5

Now that all the fractions have the same denominator (**24**), we can compare them by looking at their numerators.We have 3924\frac{39}{24}2439​, 4024\frac{40}{24}2440​, and 4224\frac{42}{24}2442​.

STEP 6

The numerators are **39**, **40**, and **42**.Since 39<40<4239 < 40 < 4239<40<42, we know that 3924<4024<4224\frac{39}{24} < \frac{40}{24} < \frac{42}{24}2439​<2440​<2442​.

STEP 7

Substituting back the original fractions, we get 138<53<74\frac{13}{8} < \frac{5}{3} < \frac{7}{4}813​<35​<47​.

STEP 8

This matches option A!

STEP 9

The correct expression is A: 138<53<74\frac{13}{8} < \frac{5}{3} < \frac{7}{4}813​<35​<47​.

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Start learning now

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Question5th Grade: Unit 4 Study Guide - Test on Thursday, DeC. 17, 24
3. Which expression is true? How do you know? A. $\frac{13}{8}<\frac{5}{3}<\frac{7}{4}$ B. $\frac{13}{8}>\frac{5}{3}>\frac{7}{4}$

What is this asking? Which of these lists of fractions is in the correct order, from smallest to largest or largest to smallest? Watch out! Don't just guess based on how the fractions look.
We need to actually compare them!

1. Convert to a Common Denominator
2. Compare the Fractions
3. Determine the Correct Order

Now that all the fractions have the same denominator (24), we can compare them by looking at their numerators.
We have $\frac{39}{24}$ , $\frac{40}{24}$ , and $\frac{42}{24}$ .

The numerators are 39, 40, and 42.
Since $39 < 40 < 42$ , we know that $\frac{39}{24} < \frac{40}{24} < \frac{42}{24}$ .

Substituting back the original fractions, we get $\frac{13}{8} < \frac{5}{3} < \frac{7}{4}$ .

The correct expression is A: $\frac{13}{8} < \frac{5}{3} < \frac{7}{4}$ .