Year 7 Mathematics: Operations, BIDMAS, Fractions, and Directed Numbers

A comprehensive set of 50 vocabulary flashcards covering Year 7 Maths topics: Rounding and Estimating, Fractions, BIDMAS/Order of Operations, and Directed Numbers.

First Significant Figure

The first non-zero digit when reading from left to right.

Rounding Up Rule

Add 1 to the target digit if the next digit is 5 or greater.

Rounding Down Rule

Keep the target digit the same if the next digit is 4 or less.

Estimation Method

Round every number in the question to 1 significant figure first, then calculate.

Fraction of an Amount Rule

Divide the amount by the denominator (bottom) then multiply by the numerator (top).

Multiplying Fractions Rule

Multiply the top numbers together and multiply the bottom numbers together.

Adding and Subtracting Fractions Rule

Find a common denominator so the bottom numbers match.

Mixed Number to Improper Fraction Rule

Multiply the whole number by the bottom digit, then add the top digit.

BIDMAS Order

The mathematical order of operations: Brackets, Indices (powers/roots), Division and Multiplication, Addition and Subtraction.

Indices (BIDMAS)

Powers like squared or cubed, and roots like square roots.

Rounding $0.03241$ to 2 Significant Figures

Rounding $0.03241$ to two significant figures yields $0.032$.

Rounding $2.009\,\text{m}$ to 2 Significant Figures

Rounding $2.009\,\text{m}$ to two significant figures yields $2.0\,\text{m}$.

Rounding $0.007249$ to 2 Significant Figures

Rounding $0.007249$ to two significant figures yields $0.0072$.

Rounding $0.08351$ to 1 Significant Figure

Rounding $0.08351$ to one significant figure yields $0.08$.

Rounding $0.853\,\text{km}$ to 1 Significant Figure

Rounding $0.853\,\text{km}$ to one significant figure yields $0.9\,\text{km}$.

Estimating $78 \times 92$

Rounding each factor to 1 significant figure gives $80 \times 90 = 7200$.

Rounding $0.1709$ to 1 Significant Figure

Rounding $0.1709$ to one significant figure yields $0.2$.

Rounding $0.00426\,\text{m}$ to 1 Significant Figure

Rounding $0.00426\,\text{m}$ to one significant figure yields $0.004\,\text{m}$.

Estimating $\frac{53 \times 17}{42}$

Rounding each number to 1 significant figure yields $\frac{50 \times 20}{40} = \frac{1000}{40} = 25$.

Estimating $\frac{24 \times 65}{0.37}$

Rounding each number to 1 significant figure yields $\frac{20 \times 70}{0.4} = \frac{1400}{0.4} = 3500$.

Estimating $98 + 11$

Rounding each value to 1 significant figure yields $100 + 10 = 110$.

Estimating $\frac{764}{19}$

Rounding each value to 1 significant figure yields $\frac{800}{20} = 40$.

Mixed Number Subtraction: $4\frac{1}{9} - 3\frac{3}{5}$

Converting to improper fractions with common denominator $45$ gives $\frac{185}{45} - \frac{162}{45} = \frac{23}{45}$.

Multiplying Fractions: $\frac{3}{11} \times \frac{4}{9}$

Multiplying numerators and denominators gives $\frac{12}{99}$, which simplifies to $\frac{4}{33}$.

Adding an Integer and a Fraction: $1 + \frac{4}{9}$

Combining gives the mixed number $1\frac{4}{9}$ or improper fraction $\frac{13}{9}$.

Multiplying Proper Fractions: $\frac{3}{4} \times \frac{5}{7}$

Multiplying numerators together and denominators together produces $\frac{15}{28}$.

Multiplying Whole Number by Fraction: $3 \times \frac{5}{11}$

Multiplying the whole number by the numerator produces $\frac{15}{11}$ (or $1\frac{4}{11}$).

Fraction of an Integer Multiplication: $\frac{3}{4} \times 12$

Evaluating gives $\frac{3 \times 12}{4} = \frac{36}{4} = 9$.

Sum of Two Numbers

To find the 'sum' of two numbers you must add them together.

Directed Multiplication: $2 \times (-7)$

Multiplying a positive number by a negative number gives $-14$.

Directed Multiplication: $(-3) \times 4$

Multiplying a negative number by a positive number gives $-12$.

Directed Multiplication: $(-5) \times (-6)$

Multiplying two negative numbers gives a positive result of $30$.

Fraction of an Amount: $\frac{1}{4} \text{ of } £42$

Dividing $£42$ by $4$ and multiplying by $1$ gives $£10.50$.

Order of Operations Calculation: $38 - 27 \div 3$

Dividing before subtracting yields $38 - 9 = 29$.

BIDMAS Evaluation: $3 \times 4 + 5$

Performing multiplication first gives $12 + 5 = 17$.

Correcting Equation with Brackets: $6 \times 2 + 5 = 42$

Adding brackets around the addition gives $6 \times (2 + 5) = 42$.

Correcting Equation with Brackets: $40 \div 4 + 6 - 2 = 2$

Adding brackets around the addition gives $40 \div (4 + 6) - 2 = 2$.

BIDMAS with Exponents: $5 + 2 \times 3^2$

Evaluating indices first gives $3^2 = 9$, multiplication gives $2 \times 9 = 18$, and addition yields $5 + 18 = 23$.

Cube Root Evaluation: $\sqrt[3]{27}$

The value is $3$, which multiplies by itself three times to equal $27$.

BIDMAS with Parentheses and Powers: $(14 - 2 \times 3)^2$

Calculating inside brackets gives $14 - 6 = 8$, and squaring gives $8^2 = 64$.

Directed Division: $8 \div (-2)$

Dividing a positive number by a negative number results in $-4$.

Directed Division: $(-12) \div 3$

Dividing a negative number by a positive number results in $-4$.

Directed Division: $(-15) \div (-5)$

Dividing a negative number by a negative number results in a positive quotient of $3$.

Subtracting a Negative Number: $9 - (-7)$

Subtracting a negative converts the signs to plus, resulting in $9 + 7 = 16$.

Subtracting Negatives: $(-11) - (-23)$

Rewriting the double negative as addition gives $-11 + 23 = 12$.

Multiplying Fraction by Mixed Number: $\frac{2}{3} \times 3\frac{3}{5}$

Converting $3\frac{3}{5}$ to $\frac{18}{5}$ gives $\frac{2}{3} \times \frac{18}{5} = \frac{36}{15}$, which simplifies to $\frac{12}{5}$ (or $2\frac{2}{5}$).

Adding Mixed Numbers: $2\frac{1}{2} + 2\frac{1}{4}$

Using common denominator $4$ gives $2\frac{2}{4} + 2\frac{1}{4} = 4\frac{3}{4}$ (or $\frac{19}{4}$).

Adding Fractions with Different Denominators: $\frac{2}{5} + \frac{8}{15}$

Converting $\frac{2}{5}$ to $\frac{6}{15}$ gives $\frac{6}{15} + \frac{8}{15} = \frac{14}{15}$.

Adding Proper Fraction and Mixed Number: $\frac{4}{7} + 2\frac{1}{3}$

Using common denominator $21$ gives $\frac{12}{21} + 2\frac{7}{21} = 2\frac{19}{21}$ (or $\frac{61}{21}$).

Evaluating Calculator Expression: $6^3 - (3^3 + 4^2)$

Calculating powers gives $6^3 = 216$, $3^3 = 27$, and $4^2 = 16$; inside brackets gives $27 + 16 = 43$; then $216 - 43 = 173$.