how does multiplication help us solve division? 3x 5=15, 5x3=15 , 15/3=5 and 15/5=3

Answer: Multiplication helps us solve division because division is the inverse operation of multiplication. A division problem asks 'what number, when multiplied by the divisor, gives the dividend?' Knowing the multiplication fact 3×5=153 \times 5 = 15 immediately tells us that 15÷3=515 \div 3 = 5 and 15÷5=315 \div 5 = 3.

Step-by-step solution

Step 1: Understand Multiplication as Grouping

Multiplication combines equal groups into a total amount. For instance, 3×5=153 \times 5 = 15 means combining 33 groups of 55 objects, which yields 1515 objects in total. Due to the commutative property of multiplication, 55 groups of 33 objects also make the same total of 1515.

Step 2: Understand Division as the Inverse Operation

Division is the inverse or reverse operation of multiplication. Instead of combining groups to find a total, division starts with the total amount and separates it into equal groups. Asking 15÷315 \div 3 means finding what number multiplied by 33 gives 1515.

Step 3: Use Multiplication Facts to Solve Division

Because 3×5=153 \times 5 = 15, we immediately know that 15÷3=515 \div 3 = 5 and 15÷5=315 \div 5 = 3. Whenever we solve a division problem a÷b=ca \div b = c, we can find the unknown quotient by recalling the corresponding multiplication fact b×c=ab \times c = a.

Step 4: Connect the Fact Family

Together, these 44 equations form a complete fact family relating the numbers 33, 55, and 1515. Knowing one multiplication fact enables us to solve 22 corresponding division problems directly without repeated subtraction or manual counting.

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