Reasoning topic
These questions change what the signs mean, or ask which signs make a line true. Once the line is in true signs, the arithmetic is plain.
A typical question gives new meanings for the four signs and asks for the value of the line.
If '+' means '÷', '−' means '+', '×' means '−', '÷' means '×', then what will come in place of the question mark (?) in the following equation? 240 × 72 + 8 ÷ 24 − 6 = ?
30
This is the question worked through under “How it works”.
Write the new line under the printed one, changing each sign once. Calculate nothing until it is finished.
Then solve it by BODMAS: brackets and powers first if there are any, then ÷ and × from left to right, then + and − from left to right.
The question above: 240 × 72 + 8 ÷ 24 − 6 = ?
Answer: 30
1. If 'm' stands for 9 and 'n' stands for 3, then what is the value of m ÷ n + m?
Put 9 and 3 in for m and n first. Then, which operation is done first?
12
The line is 9 ÷ 3 + 9. Division comes before addition: 9 ÷ 3 = 3, then 3 + 9 = 12. Adding first would give 9 ÷ 12, less than one.
2. Fill in the blanks with the mathematical operators that make the expression logical. 54 ___ 9 ___ 2 = 4
Try each pair of signs in turn.
÷ then −
54 ÷ 9 − 2 = 6 − 2 = 4. The others: 54 + 9 + 2 = 65, 54 + 9 − 2 = 61, and 54 + 9 × 2 = 54 + 18 = 72.
3. If the signs '−' and '÷' are interchanged and the numbers '6' and '9' are interchanged, which of the following equations is correct?
Rewrite every line in full, with both swaps, before you calculate.
6 ÷ 9 − 3 = 7
With both swaps, 6 ÷ 9 − 3 becomes 9 − 6 ÷ 3 = 9 − 2 = 7. The others do not give 7: 3 ÷ 6 − 9 becomes 3 − 9 ÷ 6 = 1.5, 3 ÷ 9 − 6 becomes 3 − 6 ÷ 9, about 2.33, and 3 − 6 ÷ 9 becomes 3 ÷ 9 − 6, below zero.
Practise Mathematical Operators in the app. The questions follow your level, and what you practise comes back just before you'd forget it.
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