Math  /  Numbers & Operations

QuestionWork out the following. a) 5+1×35+1 \times 3 e) 35÷5+235 \div 5+2 b) 112×511-2 \times 5 c) 1810÷518-10 \div 5 d) 24÷4+224 \div 4+2 i) 4+(48÷8)4+(48 \div 8) f) 3612÷436-12 \div 4 g) 2×(4+10)2 \times(4+10) h) (72)×3(7-2) \times 3 m) 2×(8+4)72 \times(8+4)-7 j) 56÷(2×4)56 \div(2 \times 4) k) (3+2)×(94)(3+2) \times(9-4) l) (87)×(6+5)(8-7) \times(6+5) q) 7+(109÷3)7+(10-9 \div 3) D) 5×68÷25 \times 6-8 \div 2 o) 18÷(912÷4)18 \div(9-12 \div 4) p) 100÷(8+3×4)100 \div(8+3 \times 4) r) 20(5×3+2)20-(5 \times 3+2) s) 48÷37×248 \div 3-7 \times 2 t) 36(7+4×4)36-(7+4 \times 4) 2 Work out the following. a) 164×(53)\frac{16}{4 \times(5-3)} b) 8+215÷3\frac{8+2}{15 \div 3} c) 4×(7+5)6+3×2\frac{4 \times(7+5)}{6+3 \times 2} d) 6+(118)75\frac{6+(11-8)}{7-5} е) 12÷(95)25÷5\frac{12 \div(9-5)}{25 \div 5} f) 8×2÷456+7\frac{8 \times 2 \div 4}{5-6+7} g) 3×321÷(125)\frac{3 \times 3}{21 \div(12-5)} h) 36÷(112)88÷2\frac{36 \div(11-2)}{8-8 \div 2}

Studdy Solution

STEP 1

1. Follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right).
2. Each expression needs to be simplified step-by-step to ensure accuracy.

STEP 2

1. Simplify each arithmetic expression by following the order of operations.
2. Calculate the final results for each simplified expression.

### High_Level_Step_1: Simplify each arithmetic expression by following the order of operations.

STEP 3

a) Simplify 5+1×35+1 \times 3
\begin{align*} 5 + 1 \times 3 &= 5 + 3 \\ &= 8 \end{align*}

STEP 4

e) Simplify 35÷5+235 \div 5 + 2
\begin{align*} 35 \div 5 + 2 &= 7 + 2 \\ &= 9 \end{align*}

STEP 5

b) Simplify 112×511-2 \times 5
\begin{align*} 11 - 2 \times 5 &= 11 - 10 \\ &= 1 \end{align*}

STEP 6

c) Simplify 1810÷518 - 10 \div 5
\begin{align*} 18 - 10 \div 5 &= 18 - 2 \\ &= 16 \end{align*}

STEP 7

d) Simplify 24÷4+224 \div 4 + 2
\begin{align*} 24 \div 4 + 2 &= 6 + 2 \\ &= 8 \end{align*}

STEP 8

i) Simplify 4+(48÷8)4 + (48 \div 8)
\begin{align*} 4 + (48 \div 8) &= 4 + 6 \\ &= 10 \end{align*}

STEP 9

f) Simplify 3612÷436 - 12 \div 4
\begin{align*} 36 - 12 \div 4 &= 36 - 3 \\ &= 33 \end{align*}

STEP 10

g) Simplify 2×(4+10)2 \times (4 + 10)
\begin{align*} 2 \times (4 + 10) &= 2 \times 14 \\ &= 28 \end{align*}

STEP 11

h) Simplify (72)×3(7 - 2) \times 3
\begin{align*} (7 - 2) \times 3 &= 5 \times 3 \\ &= 15 \end{align*}

STEP 12

m) Simplify 2×(8+4)72 \times (8 + 4) - 7
\begin{align*} 2 \times (8 + 4) - 7 &= 2 \times 12 - 7 \\ &= 24 - 7 \\ &= 17 \end{align*}

STEP 13

j) Simplify 56÷(2×4)56 \div (2 \times 4)
\begin{align*} 56 \div (2 \times 4) &= 56 \div 8 \\ &= 7 \end{align*}

STEP 14

k) Simplify (3+2)×(94)(3 + 2) \times (9 - 4)
\begin{align*} (3 + 2) \times (9 - 4) &= 5 \times 5 \\ &= 25 \end{align*}

STEP 15

l) Simplify (87)×(6+5)(8 - 7) \times (6 + 5)
\begin{align*} (8 - 7) \times (6 + 5) &= 1 \times 11 \\ &= 11 \end{align*}

STEP 16

q) Simplify 7+(109÷3)7 + (10 - 9 \div 3)
\begin{align*} 7 + (10 - 9 \div 3) &= 7 + (10 - 3) \\ &= 7 + 7 \\ &= 14 \end{align*}

STEP 17

D) Simplify 5×68÷25 \times 6 - 8 \div 2
\begin{align*} 5 \times 6 - 8 \div 2 &= 30 - 4 \\ &= 26 \end{align*}

STEP 18

o) Simplify 18÷(912÷4)18 \div (9 - 12 \div 4)
\begin{align*} 18 \div (9 - 12 \div 4) &= 18 \div (9 - 3) \\ &= 18 \div 6 \\ &= 3 \end{align*}

STEP 19

p) Simplify 100÷(8+3×4)100 \div (8 + 3 \times 4)
\begin{align*} 100 \div (8 + 3 \times 4) &= 100 \div (8 + 12) \\ &= 100 \div 20 \\ &= 5 \end{align*}

STEP 20

r) Simplify 20(5×3+2)20 - (5 \times 3 + 2)
\begin{align*} 20 - (5 \times 3 + 2) &= 20 - (15 + 2) \\ &= 20 - 17 \\ &= 3 \end{align*}

STEP 21

s) Simplify 48÷37×248 \div 3 - 7 \times 2
\begin{align*} 48 \div 3 - 7 \times 2 &= 16 - 14 \\ &= 2 \end{align*}

STEP 22

t) Simplify 36(7+4×4)36 - (7 + 4 \times 4)
\begin{align*} 36 - (7 + 4 \times 4) &= 36 - (7 + 16) \\ &= 36 - 23 \\ &= 13 \end{align*}
### High_Level_Step_2: Calculate the final results for each simplified expression.

STEP 23

a) Simplify 164×(53)\frac{16}{4 \times (5 - 3)}
\begin{align*} \frac{16}{4 \times (5 - 3)} &= \frac{16}{4 \times 2} \\ &= \frac{16}{8} \\ &= 2 \end{align*}

STEP 24

b) Simplify 8+215÷3\frac{8 + 2}{15 \div 3}
\begin{align*} \frac{8 + 2}{15 \div 3} &= \frac{10}{5} \\ &= 2 \end{align*}

STEP 25

c) Simplify 4×(7+5)6+3×2\frac{4 \times (7 + 5)}{6 + 3 \times 2}
\begin{align*} \frac{4 \times (7 + 5)}{6 + 3 \times 2} &= \frac{4 \times 12}{6 + 6} \\ &= \frac{48}{12} \\ &= 4 \end{align*}

STEP 26

d) Simplify 6+(118)75\frac{6 + (11 - 8)}{7 - 5}
\begin{align*} \frac{6 + (11 - 8)}{7 - 5} &= \frac{6 + 3}{2} \\ &= \frac{9}{2} \\ &= 4.5 \end{align*}

STEP 27

е) Simplify 12÷(95)25÷5\frac{12 \div (9 - 5)}{25 \div 5}
\begin{align*} \frac{12 \div (9 - 5)}{25 \div 5} &= \frac{12 \div 4}{5} \\ &= \frac{3}{5} \\ &= 0.6 \end{align*}

STEP 28

f) Simplify 8×2÷456+7\frac{8 \times 2 \div 4}{5 - 6 + 7}
\begin{align*} \frac{8 \times 2 \div 4}{5 - 6 + 7} &= \frac{16 \div 4}{6} \\ &= \frac{4}{6} \\ &= \frac{2}{3} \end{align*}

STEP 29

g) Simplify 3×321÷(125)\frac{3 \times 3}{21 \div (12 - 5)}
\begin{align*} \frac{3 \times 3}{21 \div (12 - 5)} &= \frac{9}{21 \div 7} \\ &= \frac{9}{3} \\ &= 3 \end{align*}

STEP 30

h) Simplify 36÷(112)88÷2\frac{36 \div (11 - 2)}{8 - 8 \div 2}
\begin{align*} \frac{36 \div (11 - 2)}{8 - 8 \div 2} &= \frac{36 \div 9}{8 - 4} \\ &= \frac{4}{4} \\ &= 1 \end{align*}
### Final Results: \begin{align*} \text{a)} & \quad 8 \\ \text{e)} & \quad 9 \\ \text{b)} & \quad 1 \\ \text{c)} & \quad 16 \\ \text{d)} & \quad 8 \\ \text{i)} & \quad 10 \\ \text{f)} & \quad 33 \\ \text{g)} & \quad 28 \\ \text{h)} & \quad 15 \\ \text{m)} & \quad 17 \\ \text{j)} & \quad 7 \\ \text{k)} & \quad 25 \\ \text{l)} & \quad 11 \\ \text{q)} & \quad 14 \\ \text{D)} & \quad 26 \\ \text{o)} & \quad 3 \\ \text{p)} & \quad 5 \\ \text{r)} & \quad 3 \\ \text{s)} & \quad 2 \\ \text{t)} & \quad 13 \\ \text{2a)} & \quad 2 \\ \text{2b)} & \quad 2 \\ \text{2c)} & \quad 4 \\ \text{2d)} & \quad 4.5 \\ \text{2e)} & \quad 0.6 \\ \text{2f)} & \quad \frac{2}{3} \\ \text{2g)} & \quad 3 \\ \text{2h)} & \quad 1 \\ \end{align*}

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