1.3 Operations

(b) Calculate: $-18-(-9)$ [1]

(c) Calculate: $-7\times 8$ [1]

(d) Calculate: $-96÷12$ [1]

(e) Explain, using a number line or otherwise, why subtracting a negative number is equivalent to adding a positive number. [2]

(b) By 2 pm, the temperature had risen by a further $8^{\circ }\text{C}$ from the 10 am reading. Find the temperature at 2 pm. [1]

(c) By 10 pm, the temperature had fallen to $-3^{\circ }\text{C}$. Calculate the total change in temperature from 2 pm to 10 pm. [2]

(d) Calculate the mean temperature for the day using the four readings. [2]

(e) State whether the final temperature is above or below freezing point ($0^{\circ }\text{C}$). [1]

(b) Calculate: $15-6.84$ [1]

(c) Calculate: $3.06+0.85+2.4$ [2]

(d) A piece of wood is $4.35\text{ m}$ long. If $1.8\text{ m}$ is cut off, find the remaining length. [1]

(e) Explain why lining up decimal points is essential when adding or subtracting decimals. [1]

(b) Calculate: $2.4\times 1.5$ [1]

(c) Calculate: $5.6÷0.8$ [1]

(d) Calculate: $0.084÷0.04$ [2]

(e) A rectangle has length $3.5\text{ m}$ and width $2.4\text{ m}$. Calculate its area. [2]

(f) Explain the rule for placing the decimal point when multiplying two decimals. [1]

(b) Simplify: $\frac{7}{8}-\frac{1}{2}$ [2]

(c) Calculate: $2\frac{1}{3}+1\frac{3}{4}$ [3]

(d) Find the difference between $\frac{5}{6}$ and $\frac{1}{4}$. Give your answer in simplest form. [2]

(e) Explain why a common denominator is needed when adding or subtracting fractions. [1]

(b) Calculate: $\frac{4}{9}÷\frac{2}{3}$ [2]

(c) Calculate: $1\frac{1}{2}\times \frac{4}{9}$ [2]

(d) Calculate: $2\frac{2}{5}÷1\frac{1}{3}$ [3]

(e) A recipe requires $\frac{3}{4}$ cup of flour. How much flour is needed for $2\frac{1}{2}$ batches? [2]

(f) Explain why dividing by a fraction is the same as multiplying by its reciprocal. [1]

(b) Simplify: $(\frac{5}{6}-\frac{1}{3})÷\frac{1}{2}$ [3]

(c) Simplify: $\frac{3}{4}\times \frac{2}{5}+\frac{1}{2}\times \frac{3}{5}$ [3]

(d) State which operation you performed first in part (a) and explain why. [1]

(e) A tank is $\frac{2}{3}$ full of water. After using $\frac{1}{4}$ of the water, what fraction remains? [3]

(b) Calculate: $(8+6)\times 4$ [1]

(c) Calculate: $20-3^2\times 2$ [2]

(d) Calculate: $(1.5+2.5)\times 3-4.8÷1.2$ [3]

(e) Insert brackets to make this statement true: $5+3\times 4-2=18$ [1]

(f) Explain how brackets affect the value of an expression. [1]

(b) Calculate: $(\frac{1}{3}+\frac{2}{5})\times \frac{5}{6}$ [3]

(c) Calculate: $\frac{7}{8}-\frac{1}{4}÷\frac{1}{2}$ [2]

(d) Calculate: $\frac{3}{4}\times (\frac{2}{3}+\frac{1}{6})-\frac{1}{4}$ [3]

(e) State the order of operations used in part (c). [1]

(b) A group discount of $\frac{1}{5}$ off the total is applied for groups of 10 or more. Calculate the discounted price per student. [3]

(c) There are 24 students in the group. Calculate the total amount collected. [2]

(d) The transport company charges a flat fee of $\mathrm{\$}250$ for the bus regardless of passenger numbers. Calculate how much money the school has left after paying for transport. [3]

(e) Identify where addition, subtraction, multiplication, and division are each used in this problem. [4]

(b) Calculate: $(-3+5)\times 4$ [1]

(c) Calculate: $18÷(-3)-7$ [1]

(d) Calculate: $2^3-4\times (-2)$ [2]

(e) State one reason why the answers to (a) and (b) are different. [1]

(b) Find the balance after the withdrawal. [1]

(c) By how much did the balance change from the start to the end? [2]

(d) Is the final balance positive or negative? [1]

(b) Round each number in part (a) to 1 decimal place and estimate the result. [2]

(c) Compare your exact answer to your estimate. Is it reasonable? [1]

(d) State the exact answer correct to 2 decimal places. [1]

(b) Calculate: $7.2÷0.08$ [1]

(c) Calculate: $3.75\times 1.2$ [1]

(d) A number is multiplied by $0.6$ and gives $9$. Find the original number. [2]

(b) Simplify: $\frac{11}{15}-\frac{2}{5}$ [1]

(c) Write $1\frac{3}{8}$ as an improper fraction. [1]

(d) Hence find: $1\frac{3}{8}+\frac{5}{16}$ in simplest form. [2]

(b) Calculate: $\frac{7}{9}÷\frac{14}{27}$ [2]

(c) Write $2\frac{1}{4}$ as an improper fraction. [1]

(d) Hence calculate: $2\frac{1}{4}÷\frac{3}{8}$. [2]

(b) Calculate: $(\frac{5}{6}-\frac{1}{4})\times \frac{12}{7}$ [3]

(c) Calculate: $\frac{7}{8}÷(\frac{1}{2}+\frac{1}{4})$ [3]

(d) State which operation you do first in part (c) and why. [1]

(b) Calculate: $0.375+\frac{2}{3}$ and give your answer as a fraction. [2]

(c) Convert your answer in part (b) to a decimal (3 d.p.). [1]

(d) State whether the decimal in part (c) is terminating or recurring. Give a reason. [2]

(b) Calculate: $(6.4-1.2)\times 3$ [1]

(c) Calculate: $\frac{5}{6}+2\times \frac{3}{8}$ [2]

(d) Calculate: $(\frac{5}{6}+2)\times \frac{3}{8}$ [2]

(e) Explain why (c) and (d) give different answers. [1]

(b) Sugar is sold in 2-cup bags. How many bags are needed for 6 cakes? [1]

(c) Each bag costs ₹58.50. Find the total cost for the bags needed. [1]

(d) A discount of ₹15 is applied. Find the final cost. [1]

(e) The final cost is shared equally between 3 people. How much does each person pay (₹, 2 d.p.)? [2]