Ratio Worksheets | Ratio Worksheets for Teachers - Free Printable

Let's solve each part of this "Equivalent Ratios" worksheet step by step. I'll explain the reasoning and provide answers for all problems.

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Part 1: Write two equivalent ratios

We are given a ratio in the form of a fraction (like $\frac{5}{11}$), and we need to write two equivalent ratios by multiplying both numerator and denominator by the same number.

#### 1) $\frac{5}{11}$
Multiply by 2: $\frac{5 \times 2}{11 \times 2} = \frac{10}{22}$
Multiply by 3: $\frac{5 \times 3}{11 \times 3} = \frac{15}{33}$

✔ Answer: $\frac{10}{22}, \frac{15}{33}$

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#### 2) $\frac{7}{8}$
Multiply by 2: $\frac{14}{16}$
Multiply by 3: $\frac{21}{24}$

✔ Answer: $\frac{14}{16}, \frac{21}{24}$

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#### 3) $\frac{7}{4}$
Multiply by 2: $\frac{14}{8}$
Multiply by 3: $\frac{21}{12}$

✔ Answer: $\frac{14}{8}, \frac{21}{12}$

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#### 4) $\frac{11}{5}$
Multiply by 2: $\frac{22}{10}$
Multiply by 3: $\frac{33}{15}$

✔ Answer: $\frac{22}{10}, \frac{33}{15}$

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#### 5) $\frac{4}{5}$
Multiply by 2: $\frac{8}{10}$
Multiply by 3: $\frac{12}{15}$

✔ Answer: $\frac{8}{10}, \frac{12}{15}$

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#### 6) $\frac{8}{5}$
Multiply by 2: $\frac{16}{10}$
Multiply by 3: $\frac{24}{15}$

✔ Answer: $\frac{16}{10}, \frac{24}{15}$

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Part 2: Determine whether the ratios are equivalent

Two ratios are equivalent if their cross products are equal:
$\frac{a}{b} = \frac{c}{d}$ → $a \cdot d = b \cdot c$

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#### 7) $\frac{8}{7}$ and $\frac{9}{7}$
Cross multiply: $8 \times 7 = 56$, $7 \times 9 = 63$
56 ≠ 63 → ✘ Not equivalent

✔ Answer: No

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#### 8) $\frac{4}{7}$ and $\frac{3}{4}$
$4 \times 4 = 16$, $7 \times 3 = 21$
16 ≠ 21 → ✘ Not equivalent

✔ Answer: No

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#### 9) $\frac{7}{6}$ and $\frac{11}{3}$
$7 \times 3 = 21$, $6 \times 11 = 66$
21 ≠ 66 → ✘ Not equivalent

✔ Answer: No

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#### 10) $\frac{11}{10}$ and $\frac{5}{6}$
$11 \times 6 = 66$, $10 \times 5 = 50$
66 ≠ 50 → ✘ Not equivalent

✔ Answer: No

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#### 11) $\frac{5}{7}$ and $\frac{9}{2}$
$5 \times 2 = 10$, $7 \times 9 = 63$
10 ≠ 63 → ✘ Not equivalent

✔ Answer: No

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#### 12) $\frac{5}{12}$ and $\frac{4}{3}$
$5 \times 3 = 15$, $12 \times 4 = 48$
15 ≠ 48 → ✘ Not equivalent

✔ Answer: No

> Note: These are all not equivalent, which is fine — not all pairs are!

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Part 3: Use equivalent ratios to find the unknown value

We use cross multiplication to solve for the variable.

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#### 13) $\frac{2}{9} = \frac{r}{36}$
Cross multiply: $2 \times 36 = 9 \times r$
$72 = 9r$ → $r = \frac{72}{9} = 8$

✔ Answer: $r = 8$

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#### 14) $\frac{k}{24} = \frac{11}{8}$
Cross multiply: $k \times 8 = 24 \times 11$
$8k = 264$ → $k = \frac{264}{8} = 33$

✔ Answer: $k = 33$

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#### 15) $\frac{2}{5} = \frac{8}{z}$
Cross multiply: $2 \times z = 5 \times 8$
$2z = 40$ → $z = 20$

✔ Answer: $z = 20$

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#### 16) $\frac{3}{2} = \frac{15}{z}$
Cross multiply: $3 \times z = 2 \times 15$
$3z = 30$ → $z = 10$

✔ Answer: $z = 10$

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#### 17) $\frac{9}{8} = \frac{r}{16}$
Cross multiply: $9 \times 16 = 8 \times r$
$144 = 8r$ → $r = \frac{144}{8} = 18$

✔ Answer: $r = 18$

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#### 18) $\frac{7f}{7} = \frac{11}{7}$
Wait — this is written as:
$\frac{7f}{7} = \frac{11}{7}$

Simplify left side: $\frac{7f}{7} = f$
So: $f = \frac{11}{7}$

But let’s check: Is that correct?

Yes! Because $\frac{7f}{7} = f$, so $f = \frac{11}{7}$

✔ Answer: $f = \frac{11}{7}$

> Alternatively, if it was meant to be $\frac{7}{f} = \frac{11}{7}$, then:
> Cross multiply: $7 \times 7 = 11 \times f$ → $49 = 11f$ → $f = \frac{49}{11}$

But based on the way it's written: $\frac{7f}{7} = \frac{11}{7}$, simplifies directly to $f = \frac{11}{7}$

✔ Final answer: $f = \frac{11}{7}$

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✔ Final Answers Summary:

#### Part 1: Equivalent Ratios
1) $\frac{10}{22}, \frac{15}{33}$
2) $\frac{14}{16}, \frac{21}{24}$
3) $\frac{14}{8}, \frac{21}{12}$
4) $\frac{22}{10}, \frac{33}{15}$
5) $\frac{8}{10}, \frac{12}{15}$
6) $\frac{16}{10}, \frac{24}{15}$

#### Part 2: Are they equivalent?
7) No
8) No
9) No
10) No
11) No
12) No

#### Part 3: Solve for unknown
13) $r = 8$
14) $k = 33$
15) $z = 20$
16) $z = 10$
17) $r = 18$
18) $f = \frac{11}{7}$

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Let me know if you'd like this formatted as a printable answer sheet!