Question

divide fractions & mixed numbers - clue 1
crack the code by completing the division questions below. reduce (simplify) your answers and write it as a proper fraction or as a whole or mixed number! use your answers to match and place the letters in the boxes to reveal the clue. put the letter in every box that it matches your answer in (there may be more than one!) the first one has been done for you!
$\frac{7}{10} div 1\frac{1}{6} = \frac{3}{5}$ s
$\frac{5}{6} div 1\frac{1}{2} =$ r
$2 div 1\frac{1}{9} =$ i
$\frac{3}{5} div 1\frac{4}{5} = \frac{1}{3}$ a
$1\frac{1}{4} div 1\frac{3}{4} = \frac{5}{7}$ t
$1\frac{3}{4} div 1\frac{3}{4} = 1$ m
$1\frac{7}{9} div 2 =$ e
$2\frac{3}{4} div 2 =$ k
$2\frac{4}{9} div 1\frac{5}{6} =$ c
$2 div 3\frac{1}{2} =$ b
$2\frac{1}{3} div 3 =$ n
$3 div 1\frac{1}{7} =$ g
$1\frac{1}{3} div 1\frac{3}{5} =$ w
$\frac{3}{4} div 1\frac{7}{8} =$ h

Explanation:

Step1: Convert mixed to improper fractions

For division, rewrite mixed numbers as improper fractions:

• $1\frac{1}{6}=\frac{7}{6}$, $1\frac{1}{2}=\frac{3}{2}$, $1\frac{1}{9}=\frac{10}{9}$, $1\frac{4}{5}=\frac{9}{5}$
• $1\frac{1}{4}=\frac{5}{4}$, $1\frac{3}{4}=\frac{7}{4}$, $1\frac{7}{9}=\frac{16}{9}$, $2\frac{3}{4}=\frac{11}{4}$
• $2\frac{4}{9}=\frac{22}{9}$, $1\frac{5}{6}=\frac{11}{6}$, $3\frac{1}{2}=\frac{7}{2}$, $2\frac{1}{3}=\frac{7}{3}$
• $1\frac{1}{7}=\frac{8}{7}$, $1\frac{1}{3}=\frac{4}{3}$, $1\frac{3}{5}=\frac{8}{5}$, $1\frac{7}{8}=\frac{15}{8}$

Step2: Divide by multiplying by reciprocal

For each problem, replace division with multiplication by the reciprocal of the divisor, then simplify.

1. $\frac{7}{10} \div 1\frac{1}{6} = \frac{7}{10} \times \frac{6}{7} = \frac{6}{10} = \frac{3}{5}$ (S)
2. $\frac{5}{6} \div 1\frac{1}{2} = \frac{5}{6} \times \frac{2}{3} = \frac{10}{18} = \frac{5}{9}$ (R)
3. $2 \div 1\frac{1}{9} = 2 \times \frac{9}{10} = \frac{18}{10} = 1\frac{4}{5}$ (I)
4. $\frac{3}{5} \div 1\frac{4}{5} = \frac{3}{5} \times \frac{5}{9} = \frac{15}{45} = \frac{1}{3}$ (A)
5. $1\frac{1}{4} \div 1\frac{3}{4} = \frac{5}{4} \times \frac{4}{7} = \frac{20}{28} = \frac{5}{7}$ (T)
6. $1\frac{3}{4} \div 1\frac{3}{4} = \frac{7}{4} \times \frac{4}{7} = 1$ (M)
7. $1\frac{7}{9} \div 2 = \frac{16}{9} \times \frac{1}{2} = \frac{16}{18} = \frac{8}{9}$ (E)
8. $2\frac{3}{4} \div 2 = \frac{11}{4} \times \frac{1}{2} = \frac{11}{8} = 1\frac{3}{8}$ (K)
9. $2\frac{4}{9} \div 1\frac{5}{6} = \frac{22}{9} \times \frac{6}{11} = \frac{132}{99} = \frac{4}{3} = 1\frac{1}{3}$ (C)
10. $2 \div 3\frac{1}{2} = 2 \times \frac{2}{7} = \frac{4}{7}$ (B)
11. $2\frac{1}{3} \div 3 = \frac{7}{3} \times \frac{1}{3} = \frac{7}{9}$ (N)
12. $3 \div 1\frac{1}{7} = 3 \times \frac{7}{8} = \frac{21}{8} = 2\frac{5}{8}$ (G)
13. $1\frac{1}{3} \div 1\frac{3}{5} = \frac{4}{3} \times \frac{5}{8} = \frac{20}{24} = \frac{5}{6}$ (W)
14. $\frac{3}{4} \div 1\frac{7}{8} = \frac{3}{4} \times \frac{8}{15} = \frac{24}{60} = \frac{2}{5}$ (H)

Step3: Match answers to letter boxes

Map each simplified fraction to its corresponding letter, then fill the empty boxes:

• $\frac{4}{7}$ → B (top middle empty box)
• $\frac{11}{8}=1\frac{3}{8}$ → K (top right empty box)
• $\frac{2}{5}$ → H (left middle first empty box)
• $\frac{7}{9}$ → N (left middle last empty box)
• $\frac{5}{6}$ → W (right middle first empty box)
• $\frac{7}{9}$ → N (S-E-E empty box)
• $\frac{5}{6}$ → W (bottom right first empty box)
• $\frac{7}{9}$ → N (bottom right second empty box)
• $2\frac{5}{8}$ → G (bottom right last empty box)
• $\frac{5}{6}$ → W (bottom left first empty box)
• $1\frac{1}{3}$ → C (bottom left third empty box)
• $\frac{2}{5}$ → H (bottom left last empty box)

Answer:

Completed fraction division results (with matching letters):

1. $\frac{7}{10} \div 1\frac{1}{6} = \boldsymbol{\frac{3}{5}}$ (S)
2. $\frac{5}{6} \div 1\frac{1}{2} = \boldsymbol{\frac{5}{9}}$ (R)
3. $2 \div 1\frac{1}{9} = \boldsymbol{1\frac{4}{5}}$ (I)
4. $\frac{3}{5} \div 1\frac{4}{5} = \boldsymbol{\frac{1}{3}}$ (A)
5. $1\frac{1}{4} \div 1\frac{3}{4} = \boldsymbol{\frac{5}{7}}$ (T)
6. $1\frac{3}{4} \div 1\frac{3}{4} = \boldsymbol{1}$ (M)
7. $1\frac{7}{9} \div 2 = \boldsymbol{\frac{8}{9}}$ (E)
8. $2\frac{3}{4} \div 2 = \boldsymbol{1\frac{3}{8}}$ (K)
9. $2\frac{4}{9} \div 1\frac{5}{6} = \boldsymbol{1\frac{1}{3}}$ (C)
10. $2 \div 3\frac{1}{2} = \boldsymbol{\frac{4}{7}}$ (B)
11. $2\frac{1}{3} \div 3 = \boldsymbol{\frac{7}{9}}$ (N)
12. $3 \div 1\frac{1}{7} = \boldsymbol{2\frac{5}{8}}$ (G)
13. $1\frac{1}{3} \div 1\frac{3}{5} = \boldsymbol{\frac{5}{6}}$ (W)
14. $\frac{3}{4} \div 1\frac{7}{8} = \boldsymbol{\frac{2}{5}}$ (H)

Final decoded clue (filled boxes):
HEARTBREAK, HEARTMAN, WAS, SEEN, WEARTING, WATCH