Question

3/4 + 5/12, 7/8 + 1/3, 1 15/77, 1 5/14, 5/6 + 7/10, 1/5 + 2/9, 19/45, 1 5/24, 10/11 + 2/7, 1/4 + 2/3, 1 8/15, 11/12, 2/5 + 9/10, 6/7 + 1/2, 1 3/10, 1 1/6

Explanation:

Step1: Simplify $\frac{3}{4}+\frac{5}{12}$

Find a common denominator, which is 12. Convert $\frac{3}{4}$ to $\frac{9}{12}$. Then add: $\frac{9}{12}+\frac{5}{12}=\frac{14}{12}=\frac{7}{6}=1\frac{1}{6}$. Wait, no, wait, let's recalculate. Wait, $\frac{3}{4}$ is $\frac{9}{12}$, plus $\frac{5}{12}$ is $\frac{14}{12}=\frac{7}{6}=1\frac{1}{6}$? Wait, no, the right side has $1\frac{1}{6}$? Wait, the yellow arrows: let's check each blue arrow's sum.

First blue arrow: $\frac{3}{4}+\frac{5}{12}$. Common denominator 12: $\frac{9}{12}+\frac{5}{12}=\frac{14}{12}=\frac{7}{6}=1\frac{1}{6}$. Wait, the yellow arrows: one of them is $1\frac{1}{6}$? Wait, the last row's right yellow arrow is $1\frac{1}{6}$? Wait, maybe I made a mistake. Let's do each blue arrow:

1. $\frac{3}{4}+\frac{5}{12}$:
- Common denominator 12: $\frac{3\times3}{4\times3}+\frac{5}{12}=\frac{9}{12}+\frac{5}{12}=\frac{14}{12}=\frac{7}{6}=1\frac{1}{6}$. Wait, but the yellow arrows: let's check the options. Wait, maybe the problem is to match each blue arrow (fraction addition) to the correct yellow arrow (sum). Let's do each:

First row, first blue: $\frac{3}{4}+\frac{5}{12}=\frac{9 + 5}{12}=\frac{14}{12}=\frac{7}{6}=1\frac{1}{6}$. Wait, the yellow arrows: the last row's right is $1\frac{1}{6}$? Wait, no, last row blue: $\frac{2}{5}+\frac{9}{10}=\frac{4}{10}+\frac{9}{10}=\frac{13}{10}=1\frac{3}{10}$, which matches the yellow arrow $1\frac{3}{10}$. Let's do each:

- $\frac{3}{4}+\frac{5}{12}$:
- Step1: Find LCD of 4 and 12, which is 12.
- Step2: Convert $\frac{3}{4}$ to $\frac{9}{12}$.
- Step3: Add $\frac{9}{12}+\frac{5}{12}=\frac{14}{12}=\frac{7}{6}=1\frac{1}{6}$. Wait, but the yellow arrows: is there a $1\frac{1}{6}$? The last row, right yellow: $1\frac{1}{6}$. Wait, maybe the last blue arrow in the last row is $\frac{6}{7}+\frac{1}{2}$: $\frac{12}{14}+\frac{7}{14}=\frac{19}{14}=1\frac{5}{14}$, which matches the first row's right yellow arrow $1\frac{5}{14}$.

Let's do each blue arrow:

1. $\frac{3}{4}+\frac{5}{12}$:
- LCD 12: $\frac{9}{12}+\frac{5}{12}=\frac{14}{12}=\frac{7}{6}=1\frac{1}{6}$. Wait, but the yellow arrows: the last row's right is $1\frac{1}{6}$? Wait, no, last row blue: $\frac{2}{5}+\frac{9}{10}=\frac{4}{10}+\frac{9}{10}=\frac{13}{10}=1\frac{3}{10}$, which matches the yellow arrow $1\frac{3}{10}$ (third row, left yellow? Wait, third row left yellow is $1\frac{8}{15}$? No, last row yellow is $1\frac{3}{10}$. Yes, $\frac{2}{5}+\frac{9}{10}=\frac{4 + 9}{10}=\frac{13}{10}=1\frac{3}{10}$, which matches the yellow arrow $1\frac{3}{10}$.

2. $\frac{7}{8}+\frac{1}{3}$:
- LCD 24: $\frac{21}{24}+\frac{8}{24}=\frac{29}{24}=1\frac{5}{24}$. Which matches the second row's right yellow arrow $1\frac{5}{24}$.

3. $\frac{5}{6}+\frac{7}{10}$:
- LCD 30: $\frac{25}{30}+\frac{21}{30}=\frac{46}{30}=\frac{23}{15}=1\frac{8}{15}$. Which matches the third row's left yellow arrow $1\frac{8}{15}$.

4. $\frac{1}{5}+\frac{2}{9}$:
- LCD 45: $\frac{9}{45}+\frac{10}{45}=\frac{19}{45}$. Which matches the second row's left yellow arrow $\frac{19}{45}$.

5. $\frac{10}{11}+\frac{2}{7}$:
- LCD 77: $\frac{70}{77}+\frac{22}{77}=\frac{92}{77}=1\frac{15}{77}$. Which matches the first row's left yellow arrow $1\frac{15}{77}$.

6. $\frac{1}{4}+\frac{2}{3}$:
- LCD 12: $\frac{3}{12}+\frac{8}{12}=\frac{11}{12}$. Which matches the third row's right yellow arrow $\frac{11}{12}$.

7. $\frac{2}{5}+\frac{9}{10}$:
- LCD 10: $\frac{4}{10}+\frac{9}{10}=\frac{13}{10}=1\frac{3}{10}$. Which matches the last row's left yellow arrow $1\frac{3}{10}$.

8. $\frac{6}{7}+\frac{1}{2}$:
- LCD 14: $\frac{12}{14}+\frac{7}{14}=\frac{19}{14}=1\frac{5}{14}$. Which matches the first row's right yellow arrow $1\frac{5}{14}$.

So the matching is:

- $\frac{3}{4}+\frac{5}{12}$ → $1\frac{1}{6}$ (wait, no, earlier calculation was wrong? Wait, $\frac{3}{4}+\frac{5}{12}$: 3/4 is 0.75, 5/12 ≈0.416, sum≈1.166, which is 7/6≈1.166, which is 1 1/6. But in the yellow arrows, the last row's right is 1 1/6. Wait, maybe I missed that. Let's confirm each:

1. $\frac{3}{4}+\frac{5}{12}$: 7/6 = 1 1/6 → matches $1\frac{1}{6}$ (last row, right yellow).

2. $\frac{7}{8}+\frac{1}{3}$: 29/24 = 1 5/24 → matches $1\frac{5}{24}$ (second row, right yellow).

3. $\frac{5}{6}+\frac{7}{10}$: 46/30 = 23/15 = 1 8/15 → matches $1\frac{8}{15}$ (third row, left yellow).

4. $\frac{1}{5}+\frac{2}{9}$: 19/45 → matches $\frac{19}{45}$ (second row, left yellow).

5. $\frac{10}{11}+\frac{2}{7}$: 92/77 = 1 15/77 → matches $1\frac{15}{77}$ (first row, left yellow).

6. $\frac{1}{4}+\frac{2}{3}$: 11/12 → matches $\frac{11}{12}$ (third row, right yellow).

7. $\frac{2}{5}+\frac{9}{10}$: 13/10 = 1 3/10 → matches $1\frac{3}{10}$ (last row, left yellow).

8. $\frac{6}{7}+\frac{1}{2}$: 19/14 = 1 5/14 → matches $1\frac{5}{14}$ (first row, right yellow).

So each blue arrow is matched to the correct yellow arrow by calculating the sum of the fractions (finding common denominator, adding numerators, simplifying, converting to mixed number if needed) and then matching to the yellow arrow's value.

Answer:

The matches are:

• $\boldsymbol{\frac{3}{4}+\frac{5}{12}

ightarrow 1\frac{1}{6}}$ (last row, right yellow)

• $\boldsymbol{\frac{7}{8}+\frac{1}{3}

ightarrow 1\frac{5}{24}}$ (second row, right yellow)

• $\boldsymbol{\frac{5}{6}+\frac{7}{10}

ightarrow 1\frac{8}{15}}$ (third row, left yellow)

• $\boldsymbol{\frac{1}{5}+\frac{2}{9}

ightarrow \frac{19}{45}}$ (second row, left yellow)

• $\boldsymbol{\frac{10}{11}+\frac{2}{7}

ightarrow 1\frac{15}{77}}$ (first row, left yellow)

• $\boldsymbol{\frac{1}{4}+\frac{2}{3}

ightarrow \frac{11}{12}}$ (third row, right yellow)

• $\boldsymbol{\frac{2}{5}+\frac{9}{10}

ightarrow 1\frac{3}{10}}$ (last row, left yellow)

• $\boldsymbol{\frac{6}{7}+\frac{1}{2}

ightarrow 1\frac{5}{14}}$ (first row, right yellow)

(If the question was to match each, these are the correct pairings.)