Math: adding mixed numerals, part II

Tutoring math, you meet adults upgrading for new careers.  The tutor continues with this topic, which is common on entrance tests.

If you saw my last post, you’ll recall my talk about adding mixed numerals. We covered the more difficult way last time; now we’ll do the easier way.

Example: add 325 + 467

Step 1: Convert the mixed numerals to improper fractions.

Recall that to do so, you multiply the whole number by the denominator, add the numerator, then put the answer over top the same denominator:

3 2/5 = (3×5+2)/5 = 17/5

Similarly,

4 6/7 = 34/7

Our problem is now transformed into

17/5 + 34/7

Step 2: Add the improper fractions.

As always when adding fractions, we need common denominators.

(17×7)/(5×7) + (34×5)/(7×5) = 119/35 + 170/35 = 289/35

Step 3: We would reduce if 289 and 35 shared a common factor, but they do not. If desired, we can put the answer back into a mixed numeral. We divide 289 by 35 to get 8 remainder 9. 8 becomes the whole number part of the mixed numeral, while 9 goes back over 35:

289/35 = 8 9/35

A few points:

1) Although this method is more straightforward than the previous one, it does lead to handling bigger numbers. If big numbers bother you, you’ll likely prefer the previous method.

2) From grade 11 on, you rarely see mixed numerals in academic math; improper fractions are preferred. However, trades math continues to prefer mixed numerals.

3) If a question was posed in mixed numeral form, you are likely expected to give your final answer as a mixed numeral if possible.

I’ll be covering other operations with mixed numerals in future posts.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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