Technique 6 of 21
Special multipliers: 5, 15, 25, 50, 75, 125
विशेष गुणक: 5, 15, 25, 50, 75, 125
Replace each of these multiplications with a halving or quartering followed by a shift of zeros.
When to use it · कब उपयोग करें
Whenever one number is 5, 15, 25, 50, 75 or 125 (or a multiple of these in a data-interpretation calculation).
जब भी कोई संख्या 5, 15, 25, 50, 75 या 125 हो (या डेटा इंटरप्रिटेशन गणना में इनका गुणज)।
The method · विधि
× 5, × 50 · × 5, × 50
× 5 = halve, then × 10. 48 × 5 = 24 × 10 = 240. 37 × 5 = 18.5 × 10 = 185. × 50 = halve, then × 100: 74 × 50 = 3700.
× 5 = आधा करें, फिर × 10। 48 × 5 = 24 × 10 = 240। 37 × 5 = 18.5 × 10 = 185। × 50 = आधा करें, फिर × 100: 74 × 50 = 3700।
× 25, × 75 · × 25, × 75
× 25 = divide by 4, then × 100. 52 × 25 = 13 × 100 = 1300; 47 × 25 = 11.75 × 100 = 1175. × 75 = take three-quarters, then × 100: 48 × 75 = 36 × 100 = 3600.
× 25 = 4 से भाग दें, फिर × 100। 52 × 25 = 13 × 100 = 1300; 47 × 25 = 11.75 × 100 = 1175। × 75 = तीन-चौथाई लें, फिर × 100: 48 × 75 = 36 × 100 = 3600।
× 125 · × 125
× 125 = divide by 8, then × 1000. 72 × 125 = 9 × 1000 = 9000; 64 × 125 = 8000.
× 125 = 8 से भाग दें, फिर × 1000। 72 × 125 = 9 × 1000 = 9000; 64 × 125 = 8000।
× 15 and doubling-halving · × 15 और दुगना-आधा
× 15 = the number plus half of it, then × 10: 36 × 15 = (36 + 18) × 10 = 540. Doubling-halving: 16 × 35 = 8 × 70 = 560; 25 × 48 = 100 × 12 = 1200.
× 15 = संख्या में उसका आधा जोड़कर × 10: 36 × 15 = (36 + 18) × 10 = 540। दुगना-आधा: 16 × 35 = 8 × 70 = 560; 25 × 48 = 100 × 12 = 1200।
Worked examples · हल किए उदाहरण
- 48 ÷ 2 = 24
- × 10 = 240
- 74 ÷ 2 = 37
- × 100 = 3700
- 47 ÷ 4 = 11.75
- × 100 = 1175
- Three-quarters of 48 = 36
- × 100 = 3600
- 72 ÷ 8 = 9
- × 1000 = 9000
- 36 + 18 = 54
- × 10 = 540
- Halve 16, double 35
- 8 × 70 = 560
Why it works · यह क्यों काम करता है
5 = 10 ÷ 2, 25 = 100 ÷ 4, 125 = 1000 ÷ 8, 75 = 100 × 3 ÷ 4 and 15 = 10 + 5. Dividing by a power of 2 is easier than multiplying by an awkward number.
5 = 10 ÷ 2, 25 = 100 ÷ 4, 125 = 1000 ÷ 8, 75 = 100 × 3 ÷ 4 और 15 = 10 + 5। 2 की घात से भाग देना किसी असुविधाजनक संख्या से गुणा करने से आसान है।
Do not forget the zeros you moved: × 25 is ÷ 4 and then × 100, not × 10.
जो शून्य आपने हटाए हैं उन्हें न भूलें: × 25 का मतलब ÷ 4 और फिर × 100, × 10 नहीं।
The decimal step (47 ÷ 4 = 11.75) costs a second. If the number is not a multiple of 4, keep the decimal in your head and shift it with the zeros.
दशमलव चरण (47 ÷ 4 = 11.75) में एक सेकंड लगता है। यदि संख्या 4 का गुणज नहीं है, तो दशमलव मन में रखें और शून्यों के साथ खिसका दें।
Practise this technique Practice questions are part of the Pro Pass; a few samples are free.
Related techniques
Open the cheat sheets for squares, cubes, fractions and divisibility rules.