Flashcards · 10 cards

Number foundations & fractions

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Know it
How do you add $\frac12 + \frac13$ ?
Answer
Change to the same denominator first: $\frac36 + \frac26 = \frac56$ . Never add the tops and add the bottoms.
From the lesson: Fractions and ratio
Know it
How do you divide by a fraction?
Answer
Multiply by it turned upside down: $\frac{15}{4} \div \frac34 = \frac{15}{4} \times \frac43 = 5$ .
From the lesson: Fractions and ratio
Know it
In what order do you work out a calculation with brackets, powers, ×, ÷, + and −?
Answer
Brackets, then powers, then × and ÷ (left to right), then + and − (left to right).
From the lesson: Fractions and ratio
Rule
"She spent $\frac25$ of the remainder." A fraction of what?
Answer
Of what is left, not of the whole. Work out the remainder first, then take the fraction of it.
A fraction of the remainderTake the fraction of what's left, not of the whole
From the lesson: Fractions and ratio
Rule
$a : b = 2 : 3$ and $b : c = 4 : 5$ . How do you find $a : b : c$ ?
Answer
Make the shared letter the same size in both: $a : b = 8 : 12$ and $b : c = 12 : 15$ , so $a : b : c = 8 : 12 : 15$ .
Combining two ratiosMake the shared letter the same size in both
From the lesson: Fractions and ratio
Rule
Speed, distance and time: the three formulas?
Answer
$D = S \times T$ , $S = \dfrac{D}{T}$ and $T = \dfrac{D}{S}$ .
Speed, distance, timeD = S × T, S = D ÷ T, T = D ÷ S
From the lesson: Fractions and ratio
Rule
How do you find an average speed for a whole journey?
Answer
Total distance ÷ total time. Not the average of the speeds.
Average speedTotal distance ÷ total time, not the average of the speeds
From the lesson: Fractions and ratio
Rule
How do you write 360 as a product of primes?
Answer
Split it with a factor tree until every branch ends in a prime: $360 = 2^3 \times 3^2 \times 5$ .
A factor treeSplit until every branch ends in a prime
From the lesson: Fractions and ratio
Rule
How do you find the HCF and the LCM from prime factors?
Answer
HCF: the primes they share, each to its lowest power. LCM: every prime that appears, each to its highest power.
HCF and LCMCommon primes give the HCF; all of them give the LCM
From the lesson: Fractions and ratio
Which method?
WAEC 2017 · Paper 2 · Q1 (a)
Simplify: $\dfrac{2\frac12 + 1\frac34 \div 1\frac25}{2\frac14 - 1\frac12}$ .
Where do you start?
Answer
Change the mixed numbers to improper fractions. Then do the top: divide before you add, so $1\frac34 \div 1\frac25$ comes first. Then the bottom, then divide top by bottom.
From the lesson: Fractions and ratio Try the question