12 multiple-choice questions, progressively harder.
Find 23×45\frac{2}{3} \times \frac{4}{5}32×54.
Solution
Correct answer: B
Multiply the numerators together and the denominators together.
23×45=2×43×5=815\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}32×54=3×52×4=158
Since 888 and 151515 share no factor above 111, 815\frac{8}{15}158 is already in lowest terms. Adding the tops and bottoms would give 68\frac{6}{8}86, which is wrong.
Find 12×35\frac{1}{2} \times \frac{3}{5}21×53.
Correct answer: A
12×35=1×32×5=310\frac{1}{2} \times \frac{3}{5} = \frac{1 \times 3}{2 \times 5} = \frac{3}{10}21×53=2×51×3=103
The numerator 333 and the denominator 101010 share no factor above 111, so this is in lowest terms.
Find 27×13\frac{2}{7} \times \frac{1}{3}72×31.
Correct answer: C
27×13=2×17×3=221\frac{2}{7} \times \frac{1}{3} = \frac{2 \times 1}{7 \times 3} = \frac{2}{21}72×31=7×32×1=212
Adding the tops and bottoms would give 310\frac{3}{10}103, which is wrong: multiplication never adds the denominators.
Find 34×15\frac{3}{4} \times \frac{1}{5}43×51.
Correct answer: D
34×15=3×14×5=320\frac{3}{4} \times \frac{1}{5} = \frac{3 \times 1}{4 \times 5} = \frac{3}{20}43×51=4×53×1=203
Multiplying diagonally instead would give 154\frac{15}{4}415, which is wrong.
Find 25×23\frac{2}{5} \times \frac{2}{3}52×32.
25×23=2×25×3=415\frac{2}{5} \times \frac{2}{3} = \frac{2 \times 2}{5 \times 3} = \frac{4}{15}52×32=5×32×2=154
Since 444 and 151515 share no factor above 111, 415\frac{4}{15}154 is in lowest terms.
Find 13×45\frac{1}{3} \times \frac{4}{5}31×54.
13×45=1×43×5=415\frac{1}{3} \times \frac{4}{5} = \frac{1 \times 4}{3 \times 5} = \frac{4}{15}31×54=3×51×4=154
The numerator 444 and the denominator 151515 share no factor above 111, so this is in lowest terms.
Find 3×273 \times \frac{2}{7}3×72.
Write the whole number as a fraction over 111: 3=313 = \frac{3}{1}3=13. Then multiply straight across.
31×27=3×21×7=67\frac{3}{1} \times \frac{2}{7} = \frac{3 \times 2}{1 \times 7} = \frac{6}{7}13×72=1×73×2=76
Adding 333 and 222 instead of multiplying would give 57\frac{5}{7}75, which is wrong.
Find 14×35\frac{1}{4} \times \frac{3}{5}41×53.
14×35=1×34×5=320\frac{1}{4} \times \frac{3}{5} = \frac{1 \times 3}{4 \times 5} = \frac{3}{20}41×53=4×51×3=203
Since 333 and 202020 share no factor above 111, 320\frac{3}{20}203 is in lowest terms.
Find 56×17\frac{5}{6} \times \frac{1}{7}65×71.
56×17=5×16×7=542\frac{5}{6} \times \frac{1}{7} = \frac{5 \times 1}{6 \times 7} = \frac{5}{42}65×71=6×75×1=425
The numerator 555 and the denominator 424242 share no factor above 111, so this is in lowest terms.
Find 59×12\frac{5}{9} \times \frac{1}{2}95×21.
59×12=5×19×2=518\frac{5}{9} \times \frac{1}{2} = \frac{5 \times 1}{9 \times 2} = \frac{5}{18}95×21=9×25×1=185
The numerator 555 and the denominator 181818 share no factor above 111, so this is in lowest terms.
Find 12×57\frac{1}{2} \times \frac{5}{7}21×75.
12×57=1×52×7=514\frac{1}{2} \times \frac{5}{7} = \frac{1 \times 5}{2 \times 7} = \frac{5}{14}21×75=2×71×5=145
Since 555 and 141414 share no factor above 111, 514\frac{5}{14}145 is in lowest terms.
Find 14×13\frac{1}{4} \times \frac{1}{3}41×31.
14×13=1×14×3=112\frac{1}{4} \times \frac{1}{3} = \frac{1 \times 1}{4 \times 3} = \frac{1}{12}41×31=4×31×1=121
Adding the tops and bottoms would give 27\frac{2}{7}72, which is wrong.
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