S k i l l
i n
A R I T H M E T I C

Lesson 9  Section 3

# MULTIPLY MENTALLY BYROUNDING OFF

Back to Section 1

Example 1.   Multiply 3 × 98  by rounding off 98 to 100.

 Solution. 3 × 98 = 3 × 100  −  3 × 2 = 300 − 6 = 294.

We added 2 to 98 to round it off.  Therefore we must subtract 2 -- three times. We must subtract 3 × 2.  For, we added 100 three times: Lesson 5.

 6. How do we multiply mentally by rounding off? 3 × 98 = 3 × 100  −  3 × 2 Add to the multiplicand to make it a whole number or a multiple of 10.  To compensate, as many times as you multiplied, subtract from your answer whatever you added to the multiplicand.

Example 2.   You buy four pairs of stockings at \$6.95 each.  How much do you pay?

Technique.  Round off \$6.95 to \$7.00.  Then

4 × \$7.00 = \$28.00

Now, to round off, we added 5¢.  And we added 5¢ four times because we multiplied by 4.  Therefore we must subtract 5¢ four times -- we must subtract 20¢.

\$28.00 − \$.20 = \$27.80

That is,

 4 × 6.95 = 4 × (7.00 − .05) = 4 × 7.00  −  4 × .05 4 is distributed to 7.00 and to .05.

Example 3.   What is the price of 8 items that cost \$12.99 each?  What is the price of 80 such items?

Solution.  Add 1¢ and round off to \$13.00.  Then

8 × 13 = 80 + 24 = \$104

-- minus 8 cents is \$103.92.

We must subtract 8¢ because we multiplied by 8; that is, we added  1¢ eight times.

This is the price of 8 items.   As for 80 items, they will cost 10 times more.  Move the decimal point one place right:

10 × 103.92 = 1039.2 = \$1,039.20

Please "turn" the page and do some Problems.

or

Continue on to the next Lesson.

Previous Section

1st Section on Multiplication

Please make a donation to keep TheMathPage online.
Even \$1 will help.
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "http://www.themathpage.com/ARITH/mental-arithmetic-multiplication-3.htm", "fetch_time": 1501246179000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2017-30/segments/1500550967030.98/warc/CC-MAIN-20170728123647-20170728143647-00029.warc.gz", "warc_record_offset": 558334371, "warc_record_length": 3683, "token_count": 602, "char_count": 1725, "score": 4.78125, "int_score": 5, "crawl": "CC-MAIN-2017-30", "snapshot_type": "latest", "language": "en", "language_score": 0.8304568529129028, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00053-of-00064.parquet"}