HOMEWORK 3
RICKY NG
Question 3.1. 10 − 6 · 7
Solution. Multiplication comes before subtraction:
10 − 6 · 7 = 10 − 42 = −32.
Question 3.2. (10 − 6) · 7
Solution. Parentheses come before anything else:
(10 − 6) · 7 = 4 · 7 = 28.
Question 3.3. 1 − 23 +
5
6
Solution. Only addition and subtraction are here, so perform it from left to right. First,
find the common denominator, lcm(2, 6) is 6. Then,
3 5
6 3 3 5
1 − + = 1× − × +
2 6
6 2 3 6
6 9 5
2
= − + =
6 6 6
6
1
= .
3
Question 3.4. −2 − 32
Solution. Exponent comes first.
−2 − 32 = −2 − 9 = −11.
Question 3.5. (3 + 9) ÷ 3 × 4
Solution. Work inside parentheses, then carry division and multiplication from left to
right.
(3 + 9) ÷ 3 × 4 = 12 ÷ 3 × 4 = 4 × 4 = 16.
Question 3.6. 24(−2) ÷ 4 ÷ 2(−2)
Solution. It’s the best to first write down the × signs:
24 × (−2) ÷ 4 ÷ 2 × (−2).
They are all × and ÷, so we proceed from left to right:
24 × (−2) ÷ 4 ÷ 2 × (−2) = −48 ÷ 4 ÷ 2 × (−2)
= −12 ÷ 2 × (−2)
= −6 × (−2)
= 12.
1
Question 3.7 (Solution). − 53 ÷
3
10
·
10
3
Proof. These are just division and multiplication, proceed from left to right. Remember,
when dividing by a fraction, we flip and multiply:
3 10 10
−3 2 × 5 10
− ×
×
=
×
×
5
3
3
5
3
3
10
= −2 ×
3
20
=− .
3
Question 3.8.
√
16
√
3−2 16
Solution. The priority order of square-root is just like exponent, so we do it first before
addition / subtraction:
√
16
4
4
4
4
√ =
=
=
=− .
3 − 2(4)
3−8
−5
5
3 − 2 16
√
Question 3.9. 64 − (−5 + 4(23 ))
Solution. Again, parentheses -> square-root / exponent -> multiplication / division ->
addition / subtraction:
√
√
64 − (−5 + 4(23 )) = 64 − (−5 + 4(8))
= 8 − (−5 + 32)
= 8 − 27
= −19.
Question 3.10.
−2−|32 −5|
2+8÷(2·4)
Solution. The priority order of absolute value is just like parentheses. So we do it first,
then look at division and multiplication, then addition and subtraction:
−2 − |32 − 5|
−2 − |9 − 5|
=
2 + 8 ÷ (2 · 4)
2+8÷8
−2 − 4
=
2+1
−6
=
3
= −2.
2