This is from a carnige math book

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## 1 Answer

Work out the whole number part first: 2+(-3)=2-3=-1. So we keep this sum -1 till later.

Now the fractions: ½+(-¾)+⅖. We need a denominator that’s common to all three. We have 2, 4 and 5 in the denominators but, since 2 goes into 4, we only need to find what 4 and 5 go into, and we simply multiply them together: 4×5=20. 2 goes into 20 10 times; 4 goes 5 times and 5 goes 4 times, so ½=10/20, ¼=5/20 and ⅕=4/20. So ¾ is 3 times ¼=3×5/20=15/20, ⅖=2×4/20=8/20. That gives us 10+(-15)+8=10-15+8=10+8-15=3 twentieths which we write ³⁄₂₀.

Now we remember the -1 from earlier, so we have the sum -1+³⁄₂₀. We need something to represent -1. Since 1=20/20 that is, 20 twentieths, we have the sum -20+3, which is the same as -(20-3)=-17, so we have negative 17 twentieths, which we write -¹⁷⁄₂₀ as the final answer.

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