mr barton maths

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Related Calculations

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Foundational skills
Write a division from multiplication (÷ first factor)
\[ 24 \times 15 = 360 \rightarrow 360 \div 24 \]
Divide product by first factor.
Write a division from multiplication (÷ second factor)
\[ 17 \times 23 = 391 \rightarrow 391 \div 23 \]
Divide product by second factor.
Write a multiplication from division
\[ 432 \div 18 = 24 \rightarrow 18 \times 24 \]
Use inverse relationship.
Related multiplications – one factor ×10
Scale first factor by 10
\[ 34 \times 27 \rightarrow 340 \times 27 \]
First factor ×10, product ×10.
Scale second factor by 10
\[ 45 \times 18 \rightarrow 45 \times 180 \]
Second factor ×10, product ×10.
Related multiplications – one factor ×100
Scale first factor by 100
\[ 23 \times 16 \rightarrow 2300 \times 16 \]
First factor ×100, product ×100.
Scale second factor by 100
\[ 14 \times 35 \rightarrow 14 \times 3500 \]
Second factor ×100, product ×100.
Related multiplications – one factor ×1000
Scale first factor by 1000
\[ 12 \times 45 \rightarrow 12000 \times 45 \]
First factor ×1000, product ×1000.
Scale second factor by 1000
\[ 25 \times 24 \rightarrow 25 \times 24000 \]
Second factor ×1000, product ×1000.
Related multiplications – one factor ÷10
Scale first factor by ÷10 (integer)
\[ 340 \times 27 \rightarrow 34 \times 27 \]
First factor ÷10, product ÷10.
Scale second factor by ÷10 (integer)
\[ 45 \times 180 \rightarrow 45 \times 18 \]
Second factor ÷10, product ÷10.
Scale first factor by ÷10 (decimal)
\[ 23 \times 14 \rightarrow 2.3 \times 14 \]
First factor becomes decimal.
Scale second factor by ÷10 (decimal)
\[ 35 \times 24 \rightarrow 35 \times 2.4 \]
Second factor becomes decimal.
Related multiplications – both factors scaled
Both factors ×10 (product ×100)
\[ 15 \times 23 \rightarrow 150 \times 230 \]
Both ×10, so product ×100.
Both factors ×100 (product ×10,000)
\[ 12 \times 14 \rightarrow 1200 \times 1400 \]
Both ×100, so product ×10,000.
One ×10 and one ×100 (product ×1000)
\[ 14 \times 25 \rightarrow 140 \times 2500 \]
Combined scaling: ×1000.
One ×10 and one ÷10 (unchanged)
\[ 36 \times 45 \rightarrow 360 \times 4.5 \]
Effects cancel out.
One ×100 and one ÷10 (product ×10)
\[ 24 \times 35 \rightarrow 2400 \times 3.5 \]
Net effect: product ×10.
Related divisions from multiplication – dividend scaled
Dividend ×10 (from multiplication)
\[ 23 \times 18 = 414 \rightarrow 4140 \div 23 \]
Dividend ×10, quotient ×10.
Dividend ×100 (from multiplication)
\[ 15 \times 24 = 360 \rightarrow 36000 \div 15 \]
Dividend ×100, quotient ×100.
Dividend ×10 dividing by first factor
\[ a \times b = c \rightarrow 10c \div a \]
Use scaling with inverse.
Dividend ×10 dividing by second factor
\[ 17 \times 26 = 442 \rightarrow 4420 \div 26 \]
Quotient relates to first factor.
Related divisions from multiplication – divisor scaled
Divisor ×10 (quotient ÷10)
\[ 35 \times 24 = 840 \rightarrow 840 \div 350 \]
Bigger divisor, smaller quotient.
Divisor ×10 by scaled second factor
\[ 28 \times 15 = 420 \rightarrow 420 \div 150 \]
Divisor ×10, quotient ÷10.
Related divisions from multiplication – both scaled
Both ×10 (quotient unchanged)
\[ 24 \times 35 = 840 \rightarrow 8400 \div 240 \]
Same scaling cancels out.
Dividend ×100, divisor ×10 (quotient ×10)
\[ 18 \times 45 = 810 \rightarrow 81000 \div 180 \]
Net effect: quotient ×10.
Dividend ×10, divisor ×100 (quotient ÷10)
\[ 25 \times 36 = 900 \rightarrow 9000 \div 2500 \]
Net effect: quotient ÷10.
Related divisions from division facts
Dividend ×10 from division fact
\[ 756 \div 36 = 21 \rightarrow 7560 \div 36 \]
Dividend ×10, quotient ×10.
Divisor ×10 from division fact (÷10)
\[ 840 \div 24 = 35 \rightarrow 840 \div 240 \]
Divisor ×10, quotient ÷10.
Both ×10 from division fact
\[ 644 \div 28 = 23 \rightarrow 6440 \div 280 \]
Both ×10, quotient unchanged.
Dividend ×100, divisor ×10 from division
\[ 432 \div 18 = 24 \rightarrow 43200 \div 180 \]
Net effect: quotient ×10.
Dividend ÷10 from division fact
\[ 4560 \div 24 = 190 \rightarrow 456 \div 24 \]
Dividend ÷10, quotient ÷10.
Extensions
Identify the scaling applied
\[ 23 \times 17 = 391, \; 23 \times \square = 3910 \]
Find the missing scaled factor.
Identify the original multiplication
\[ 230 \times 170 = 39100 \rightarrow \text{?} \]
Find the simpler base fact.
Chain of related calculations
\[ 24 \times 35 = 840 \rightarrow 8400 \div 35 \]
Two-step: inverse + scaling.
Mixed scaling with inverse
\[ 45 \times 28 = 1260 \rightarrow 12600 \div 450 \]
Apply both scalings together.
Determine which is larger
\[ 3600 \div 25 \text{ vs } 900 \div 250 \]
Compare two related calculations.
Find the missing number
\[ 32 \times 45 = 1440, \; 14400 \div \square = 45 \]
Use relationships to find missing divisor.
Timer (Optional)
Question