Simplify: (46 × 102)+(102 × 54)

Correct Answer is : 10,20010,20010,200

Correct Answer is : 10,20010,20010,200

Test Index

BECE Mathematics 2016 Paper

Question : 10

Total: 40

Simplify:

(46 \times 102)+(102 \times 54)

Solution:

Method I

Since 102 is common in both sides, you can factorize it out and simplify

\;(46 \times 102)+(102 \times 54)=102(46+54)

\;46+54=100

\;102(46+54)=102(100)=102 \times 100

When multiplying by a number with zeros at the end, multiply the non-zero numbers and join the zeros at the end to the result obtained.

\;102 \times 100=102 \times 1 \; \text{ and result joined by two zeros } \;

\;102 \times 100=10200=10,200

Method II

Multiply each in the bracket and add the result in the brackets.

\;46 \times 102=4,692

\;102 \times 54=5,508

(46 \times 102)+(102 \times 54)=4,692+5,508=10,200

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