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Multiplication and Division of Terms Practice Questions (page 2)

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Updated on Oct 3, 2011

Practice 3

1. Begin with the coefficients: 15 ÷3 = 5. Carry the base (v) from the dividend into the answer. There are no bases in the divisor that are not in the dividend, and vice versa. Next, subtract the exponent of v in the divisor from the exponent of v in the dividend: 9 – 5 = 4. The exponent of v in the answer is 4. (15v9)(3v5) = 5v4.
2. Begin with the coefficients: –63 ÷ –7 = 9. Carry the base (a) from the dividend into the answer. There are no bases in the divisor that are not in the dividend, and vice versa. Next, subtract the exponent of a in the divisor from the exponent of a in the dividend: 1 – 8 = –7. The exponent of a in the answer is –7. (–63a)(–7a8) = 9a–7.
3. Begin with the coefficients: 30 ÷ –5 = –6. Carry the bases (p, q, and r) from the dividend into the answer. There are no bases in the divisor that are not in the dividend. Because p does not appear in the divisor, carry its exponent into the answer. Next, subtract the exponent of q in the divisor from the exponent of q in the dividend: 4 – 2 = 2. Finally, subtract the exponent of r in the divisor from the exponent of r in the dividend: 2 – 3 = –1. The exponent of r in the answer is –1. (30p11q4r2)(–5q2r3) = –6p11q2r–1.
4. Begin with the coefficients: 11 ÷ 11 = 1. Carry the bases (x and y) from the dividend into the answer. The divisor has a base (z) that is not in the dividend, so next, carry it into the answer. Change its exponent from 2 to –2. Because x does not appear in the divisor, carry its exponent into the answer. Finally, subtract the exponent of y in the divisor from the exponent of y in the dividend: 5 – 5 = 0, so our answer does not have a base of y after all. (11x3y5)(11y5z2) = x3z–2.
5. Begin with the coefficients: –42 ÷ 6 = –7. Carry the bases (m, n, and o) from the dividend into the answer. Because o does not appear in the divisor, carry its exponent into the answer. Next, subtract the exponent of m in the divisor from the exponent of m in the dividend: 2 – 1 = 1. The exponent of m in the answer is 1. Finally, subtract the exponent of n in the divisor from the exponent of n in the dividend: –2 – 2 = –4. The exponent of n in the answer is –4. (–42m2n–2o5)(6mn2) = –7mn–4o5.

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